3 Geometry, compatibility and structure preservation in computational differential equationshttp://sms.cam.ac.uk/collection/3028099
Computations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive all-purpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purpose-built algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a large-scale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of space-time discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
Compatible discretizations.
Geometric numerical integration.
Structure preservation and numerical relativity.
Applications to computations in quantum mechanics.14402019Mon, 16 Dec 2019 16:06:02 +0000Wed, 17 Jul 2019 14:42:03 +0100ensms-support@ucs.cam.ac.uk Geometry, compatibility and structure preservation in computational differential equationshttp://sms.cam.ac.uk/collection/3028099
http://rss.sms.cam.ac.uk/itunes-image/3103513.jpghttp://video.search.yahoo.com/mrss Geometry, compatibility and structure preservation in computational differential equationsComputations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive all-purpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purpose-built algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a large-scale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of space-time discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
Compatible discretizations.
Geometric numerical integration.
Structure preservation and numerical relativity.
Applications to computations in quantum mechanics. Geometry, compatibility and structure preservation in computational differential equationsComputations of differential equations are a fundamental activity in applied mathematics. While historically the main quest was to derive all-purpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purpose-built algorithms that are tailored to preserve special features of each class. This has given rise to the new fields of geometric numerical integration and of structure preserving discretization. In addition to being quantitatively accurate, these novel methods have the advantage of also being qualitatively accurate as they inherit the key structural properties of their continuum counterparts. This has meant a large-scale introduction of geometric and topological thinking into modern numerical mathematics.
During this scientific programme at the Isaac Newton Institute for Mathematical Sciences, we will address fundamental questions in the field of structure preserving discretizations of differential equations on manifolds in space and time. We will bring together two communities that have been pursuing their science along parallel tracks to endeavour breakthroughs in some major scientific applications, which call for advanced numerical simulation techniques. This will lead to the development of a new generation of space-time discretizations for evolutionary equations.
During the programme we intend to organise three workshops and two focused study periods lasting two weeks on selected application areas.
The core themes of the programme are:
Compatible discretizations.
Geometric numerical integration.
Structure preservation and numerical relativity.
Applications to computations in quantum mechanics.Cambridge UniversityK. Kherhttp://sms.cam.ac.uk/collection/3028099 Geometry, compatibility and structure preservation in computational differential equations2019-07-17T14:42:03+01:00INIMS002281no Computational Challenges in Numerical Relativityucs_sms_3028099_3071216http://sms.cam.ac.uk/media/3071216
Computational Challenges in Numerical RelativityPretorius, F
Monday 30th September 2019 - 16:00 to 17:00Mon, 30 Sep 2019 17:27:46 +0100Isaac Newton InstitutePretorius, Fcd2a54f778099decb614302c2e7a2db2979bc9c3b936f6e90f9f1d3bdc806104de29727e12e3378a157efb5ecea058bc545608e63f66795b0fde8351466994c3Pretorius, F
Monday 30th September 2019 - 16:00 to 17:00Pretorius, F
Monday 30th September 2019 - 16:00 to 17:00Cambridge University3840http://sms.cam.ac.uk/media/3071216 Computational Challenges in Numerical RelativityPretorius, F
Monday 30th September 2019 - 16:00 to 17:00I will give a brief overview of the some of the challenges in computational solution of the Einstein field equations.I will then describe the background error subtraction technique, designed to allow for more computationally efficient solution of scenarios where a significant portion of the domain is close to a know, exact solution. To demonstrate, I will discuss application to tidal disruption of a star by a supermassive black hole, and studies of black hole superradiance.2019-09-30T17:27:46+01:0038403071216true16x9falseno Equivariance and structure preservation in numerical methods; some cases and viewpointsucs_sms_3028099_3124317http://sms.cam.ac.uk/media/3124317
Equivariance and structure preservation in numerical methods; some cases and viewpointsOwren, B
Wednesday 11th December 2019 - 15:05 to 15:50Mon, 16 Dec 2019 16:06:02 +0000Isaac Newton InstituteOwren, Bc564e0df6f840a57617334f3473e4ab5908282ec48dd5793ea9f18cb7867f7c8dc77af6dc36fc473f1ec77e7c6e556366e536cec195204157e95c30f0bf0261fOwren, B
Wednesday 11th December 2019 - 15:05 to 15:50Owren, B
Wednesday 11th December 2019 - 15:05 to 15:50Cambridge University3178http://sms.cam.ac.uk/media/3124317 Equivariance and structure preservation in numerical methods; some cases and viewpointsOwren, B
Wednesday 11th December 2019 - 15:05 to 15:50Our point of departure is the situation when there is a group of transformations acting both on our problem space and on the space in which our computations are produced. Equivariance happens when the map from the problem space to the computation space, i.e. our numerical method, commutes with the group action. This is a rather general and vague definition, but we shall make it precise and consider a few concrete examples in the talk. In some cases, the equivariance property is natural, in other cases it is something that we want to impose in the numerical method in order to obtain computational schemes with certain desired structure preserving qualities. Many of the examples we present will be related to the numerical solution of differential equations and we may also present some recent examples from artificial neural networks and discrete integrable systems. This is work in progress and it summarises some of the ideas the speaker has been discussing with other participants this autumn.2019-12-16T16:06:02+00:0031783124317true16x9falseno General Relativity: One Block at a Timeucs_sms_3028099_3073190http://sms.cam.ac.uk/media/3073190
General Relativity: One Block at a TimeMiller, W
Thursday 3rd October 2019 - 13:30 to 14:30Thu, 03 Oct 2019 14:40:52 +0100Isaac Newton InstituteMiller, W82bbf81867c55a798692c99cb0b6a1eb1f9cffde38e1ff5bb95a6c036693070da448dfc180e6a4f94b3ae6978e89c9d30e219d16f43dd05d131b86645eb5ff78Miller, W
Thursday 3rd October 2019 - 13:30 to 14:30Miller, W
Thursday 3rd October 2019 - 13:30 to 14:30Cambridge University3900http://sms.cam.ac.uk/media/3073190 General Relativity: One Block at a TimeMiller, W
Thursday 3rd October 2019 - 13:30 to 14:30This talk will provide an overview and motivation for Regge calculus (RC). We will highlight our insights into unique features of building GR on a discrete geometry in regards to structure preservation, and highlight some relative strengths and weaknesses of RC. We will review some numerical applications of RC, including our more recent work on discrete Ricci flow.2019-10-03T14:40:52+01:0039003073190true16x9falseno Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.ucs_sms_3028099_3105521http://sms.cam.ac.uk/media/3105521
Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.Barp, A
Thursday 21st November 2019 - 13:05 to 13:45Fri, 22 Nov 2019 12:21:00 +0000Isaac Newton InstituteBarp, A2427f78e4c3bd735bedd84f9ea730592d65c62a645befb00095f4c54e9e63a77b3d526c160596fa1914328e67c07d7ef922a0280c96c27192604fdc3960eb54aBarp, A
Thursday 21st November 2019 - 13:05 to 13:45Barp, A
Thursday 21st November 2019 - 13:05 to 13:45Cambridge University2334http://sms.cam.ac.uk/media/3105521 Hamiltonian Monte Carlo on Homogeneous Manifolds for QCD and Statistics.Barp, A
Thursday 21st November 2019 - 13:05 to 13:452019-11-22T12:21:00+00:0023343105521true16x9falseno Hyperbolicity and boundary conditions.ucs_sms_3028099_3071760http://sms.cam.ac.uk/media/3071760
Hyperbolicity and boundary conditions.Reula, O
Tuesday 1st October 2019 - 13:30 to 14:30Tue, 01 Oct 2019 14:35:48 +0100Isaac Newton InstituteReula, Oc4cd1b3721458facfede318812d366e81532b90e3170a038e83a3fe1776e820f13497efa5592fbbcb69f4d84e7dfa7b6e2164f99e42b94c7a7981de582090707Reula, O
Tuesday 1st October 2019 - 13:30 to 14:30Reula, O
Tuesday 1st October 2019 - 13:30 to 14:30Cambridge University3600http://sms.cam.ac.uk/media/3071760 Hyperbolicity and boundary conditions.Reula, O
Tuesday 1st October 2019 - 13:30 to 14:30Abstract: (In collaboration with Fernando Abalos.) Very often in physics, the evolution systems we have to deal with are not purely hyperbolic, but contain also constraints and gauge freedoms. After fixing these gauge freedoms we obtain a new system with constraints which we want to solve subject to initial and boundary values. In particular, these values have to imply the correct propagation of constraints. In general, after fixing some reduction to a purely evolutionary system, this is asserting by computing by hand what is called the constraint subsidiary system, namely a system which is satisfied by the constraints quantities when the fields satisfy the reduced evolution system. If the subsidiary system is also hyperbolic then for the initial data case the situation is clear: we need to impose the constraints on the initial data and then they will correctly propagate along evolution. For the boundary data, we need to impose the constraint for all incoming constraint modes. These must be done by fixing some of the otherwise free boundary data, that is the incoming modes. Thus, there must be a relation between some of the incoming modes of the evolution system and all the incoming modes of the constraint subsidiary system. Under certain conditions on the constraints, this relation is known and understood, but those conditions are very restrictive. In this talk, we shall review the known results and discuss what is known so far for the general case and what are the open questions that still remain.2019-10-01T14:35:48+01:0036003071760true16x9falseno New prospects in numerical relativityucs_sms_3028099_3072353http://sms.cam.ac.uk/media/3072353
New prospects in numerical relativityWitek, H
Wednesday 2nd October 2019 - 13:30 to 14:30Wed, 02 Oct 2019 14:35:05 +0100Isaac Newton InstituteWitek, H259b563b4b00b7123e1ea1bc8f233d54cd93b8d5e2220252399d2cff8b9c3a24c2ac406cb4369831ed8520c65ab56e5a78f0fe5474011e326f9c10bc1f36570dWitek, H
Wednesday 2nd October 2019 - 13:30 to 14:30Witek, H
Wednesday 2nd October 2019 - 13:30 to 14:30Cambridge University3536http://sms.cam.ac.uk/media/3072353 New prospects in numerical relativityWitek, H
Wednesday 2nd October 2019 - 13:30 to 14:30Both observations and deeply theoretical considerations indicate that general relativity, our elegant standard model of gravity, requires modifications at high curvatures scales. Candidate theories of quantum gravity, in their low-energy limit, typically predict couplings to additional fields or extensions that involve higher curvature terms. At the same time, the breakthrough discovery of gravitational waves has provided a new channel to probe gravity in its most extreme, strong-field regime. Modelling the expected gravitational radiation in these extensions of general relativity enables us to search for - or place novel observational bounds on - deviations from our standard model. In this talk I will give an overview of the recent progress on simulating binary collisions in these situations and address renewed mathematical challenges such as well-posedness of the underlying initial value formulation.2019-10-02T14:35:05+01:0035363072353true16x9falseno Numerical relativity beyond astrophysics: new challenges and new dynamicsucs_sms_3028099_3071106http://sms.cam.ac.uk/media/3071106
Numerical relativity beyond astrophysics: new challenges and new dynamicsFigueras, P
Monday 30th September 2019 - 13:30 to 14:30Mon, 30 Sep 2019 14:39:07 +0100Isaac Newton InstituteFigueras, P2243225c6ab1bf9d6d12d3b2a3024746605bc11461d32b1ad446d946d943a77cfcadec79f2bbc859275b610dae1486ee37b5467ac3f5c41dc13ae85c9a689624Figueras, P
Monday 30th September 2019 - 13:30 to 14:30Figueras, P
Monday 30th September 2019 - 13:30 to 14:30Cambridge University3600http://sms.cam.ac.uk/media/3071106 Numerical relativity beyond astrophysics: new challenges and new dynamicsFigueras, P
Monday 30th September 2019 - 13:30 to 14:30Motivated by more fundamental theories of gravity such as string theory, in recent years there has been a growing interesting in solving the Einstein equations numerically beyond the traditional astrophysical set up. For instance in spacetime dimensions higher than the four that we have observed, or in exotic spaces such as anti-de Sitter spaces. In this talk I will give an overview of the challenges that are often encountered when solving the Einstein equations in these new settings. In the second part of the talk I will provide some examples, such as the dynamics of unstable black holes in higher dimensions and gravitational collapse in anti-de Sitter spaces.2019-09-30T14:39:07+01:0036003071106true16x9falseno Optimal control and the geometry of integrable systemsucs_sms_3028099_3036842http://sms.cam.ac.uk/media/3036842
Optimal control and the geometry of integrable systemsBloch, A
Wednesday 31st July 2019 - 15:00 to 16:00Thu, 01 Aug 2019 14:36:30 +0100Isaac Newton InstituteBloch, A3fe8298338e4ee54eda4d46363c643aa2b65bf42805791cca3868fffefcf29b49c44a9975d9faaec381d792bed2e655f6cdf188607f61e49212afeaacee2516dBloch, A
Wednesday 31st July 2019 - 15:00 to 16:00Bloch, A
Wednesday 31st July 2019 - 15:00 to 16:00Cambridge University3525http://sms.cam.ac.uk/media/3036842 Optimal control and the geometry of integrable systemsBloch, A
Wednesday 31st July 2019 - 15:00 to 16:00In this talk we discuss a geometric approach to certain optimal control
problems and discuss the relationship of the solutions of these problem
to some classical integrable dynamical systems and their generalizations.
We consider the
so-called Clebsch optimal control problem and its relationship
to Lie group actions on manifolds. The integrable systems discussed include
the rigid body equations, geodesic flows on the ellipsoid, flows
on Stiefel manifolds, and the Toda lattice
flows. We discuss the Hamiltonian structure of these systems and relate
our work to some work of Moser. We also discuss the link to discrete dynamics
and symplectic integration.2019-08-01T14:36:30+01:0035253036842true16x9falseno Putting Infinity on the Griducs_sms_3028099_3072957http://sms.cam.ac.uk/media/3072957
Putting Infinity on the GridHilditch, D
Thursday 3rd October 2019 - 11:00 to 12:00Thu, 03 Oct 2019 12:06:01 +0100Isaac Newton InstituteHilditch, Dbd352b6a06024d5faca207ed84b95ba33d841fde98dbec0ecec123bd13ff812dda6c0cd130375e423a2989fdd1ecf8aa4df7308ea2ca75f1d133d8ca12974843Hilditch, D
Thursday 3rd October 2019 - 11:00 to 12:00Hilditch, D
Thursday 3rd October 2019 - 11:00 to 12:00Cambridge University3600http://sms.cam.ac.uk/media/3072957 Putting Infinity on the GridHilditch, D
Thursday 3rd October 2019 - 11:00 to 12:00I will talk about an ongoing research program relying on a dual frame approach to treat numerically the field equations of GR (in generalized harmonic gauge) on compactified hyperboloidal slices. These slices terminate at future-null infinity, and the hope is to eventually extract gravitational waves from simulations there. The main obstacle to their use is the presence of 'infinities' coming from the compactified coordinates, which have to somehow interact well with the assumption of asymptotic flatness so that we may arrive at regular equations for regular unknowns. I will present a new 'subtract the logs' regularization strategy for a toy nonlinear wave equation that achieves this goal.2019-10-03T12:06:01+01:0036003072957true16x9falseno Some Research Problems in Mathematical and Numerical General Relativityucs_sms_3028099_3071547http://sms.cam.ac.uk/media/3071547
Some Research Problems in Mathematical and Numerical General RelativityHolst, M
Monday 30th September 2019 - 11:00 to 12:00Tue, 01 Oct 2019 09:29:14 +0100Isaac Newton InstituteHolst, M3323e902a275492ee67a983338f3b980aee04f18f7d334b98c1e2505b2f34274491b8f42b48aee6ff3f05b799d66e711f7c8525ecc45f7fcaa52e82584ecd6e2Holst, M
Monday 30th September 2019 - 11:00 to 12:00Holst, M
Monday 30th September 2019 - 11:00 to 12:00Cambridge University3780http://sms.cam.ac.uk/media/3071547 Some Research Problems in Mathematical and Numerical General RelativityHolst, M
Monday 30th September 2019 - 11:00 to 12:00The 2017 Nobel Prize in Physics was awarded to three of the key scientists involved in the development of LIGO and its eventual successful first detections of gravitational waves. How do LIGO (and other gravitational wave detector) scientists know what they are detecting? The answer is that the signals detected by the devices are shown, after extensive data analysis and numerical simulations of the Einstein equations, to be a very close match to computer simulations of wave emission from very particular types of binary collisions. In this lecture, we begin with a brief overview of the mathematical formulation of Einstein (evolution and constraint) equations, and then focus on some fundamental mathematics research questions involving the Einstein constraint equations. We begin with a look at the most useful mathematical formulation of the constraint equations, and then summarize the known existence, uniqueness, and multiplicity results through 2009. We then present a number of new existence and multiplicity results developed since 2009 that substantially change the solution theory for the constraint equations. In the second part of the talk, we consider approaches for developing "provably good" numerical methods for solving these types of geometric PDE systems on 2- and 3-manifolds. We examine how one proves rigorous error estimates for particular classes of numerical methods, including both classical finite element methods and newer methods from the finite element exterior calculus. This lecture will touch on several joint projects that span more than a decade, involving a number of collaborators. The lecture is intended both for mathematicians interested in potential research problems in mathematical and numerical general relativity, as well as physicists interested in relevant new developments in mathematical and numerical methods for nonlinear geometric PDE.2019-10-01T09:29:14+01:0037803071547true16x9falseno Structure-preserving time discretization: lessons for numerical relativity?ucs_sms_3028099_3071157http://sms.cam.ac.uk/media/3071157
Structure-preserving time discretization: lessons for numerical relativity?Stern, A
Monday 30th September 2019 - 14:30 to 15:30Mon, 30 Sep 2019 15:45:51 +0100Isaac Newton InstituteStern, Adcc5b4ed737fe671529cbdbe2274a2fd79e6ff817524c3590bccfe0274c637cd912505a93dc0335a89788990c65aae8a9acd3e4f2acf05bf36d77e32dbcd59c0Stern, A
Monday 30th September 2019 - 14:30 to 15:30Stern, A
Monday 30th September 2019 - 14:30 to 15:30Cambridge University3570http://sms.cam.ac.uk/media/3071157 Structure-preserving time discretization: lessons for numerical relativity?Stern, A
Monday 30th September 2019 - 14:30 to 15:30In numerical ODEs, there is a rich literature on methods that preserve certain geometric structures arising in physical systems, such as Hamiltonian/symplectic structure, symmetries, and conservation laws. I will give an introduction to these methods and discuss recent work extending some of these ideas to numerical PDEs in classical field theory.2019-09-30T15:45:51+01:0035703071157true16x9falseno Tetrad methods in numerical relativityucs_sms_3028099_3074059http://sms.cam.ac.uk/media/3074059
Tetrad methods in numerical relativityGarfinkle, D
Friday 4th October 2019 - 16:00 to 17:00Fri, 04 Oct 2019 17:15:40 +0100Isaac Newton InstituteGarfinkle, Dd39abe52cd1e6b823c475209925a1829ce714d4b87448f973866e4d9a0e98d96361ce4c96fb6faea611ca12e545ebfde114cad30d1dab0399bffe1e2a4df2725Garfinkle, D
Friday 4th October 2019 - 16:00 to 17:00Garfinkle, D
Friday 4th October 2019 - 16:00 to 17:00Cambridge University4080http://sms.cam.ac.uk/media/3074059 Tetrad methods in numerical relativityGarfinkle, D
Friday 4th October 2019 - 16:00 to 17:00Most numerical relativity simulations use the usual coordinate methods to put the Einstein field equations in the form of partial differential equations (PDE), which are then handled using more or less standard numerical PDE methods, such as finite differences. However, there are some advantages to instead using a tetrad (orthonormal) basis rather than the usual coordinate basis. I will present the tetrad method and its numerical uses, particularly for simulating the approach to a spacetime singularity. I will end with open questions about which tetrad systems are suitable for numerical simulations.2019-10-04T17:15:40+01:0040803074059true16x9falseno Variational discretizations of gauge field theories using group-equivariant interpolation spacesucs_sms_3028099_3071682http://sms.cam.ac.uk/media/3071682
Variational discretizations of gauge field theories using group-equivariant interpolation spacesLeok, M
Tuesday 1st October 2019 - 11:00 to 12:00Tue, 01 Oct 2019 12:03:02 +0100Isaac Newton InstituteLeok, Mef8fd2368c3a1477b969519161e5c026f4cb8d07063f135d67cfb4b51ff1c0aba5145c56938dd0b7b3cc990ff2d1199ebd0770b95f7fc4dfb647eda7c908aef5Leok, M
Tuesday 1st October 2019 - 11:00 to 12:00Leok, M
Tuesday 1st October 2019 - 11:00 to 12:00Cambridge University3600http://sms.cam.ac.uk/media/3071682 Variational discretizations of gauge field theories using group-equivariant interpolation spacesLeok, M
Tuesday 1st October 2019 - 11:00 to 12:00Variational integrators are geometric structure-preserving numerical methods that preserve the symplectic structure, satisfy a discrete Noether's theorem, and exhibit exhibit excellent long-time energy stability properties. An exact discrete Lagrangian arises from Jacobi's solution of the Hamilton-Jacobi equation, and it generates the exact flow of a Lagrangian system. By approximating the exact discrete Lagrangian using an appropriate choice of interpolation space and quadrature rule, we obtain a systematic approach for constructing variational integrators. The convergence rates of such variational integrators are related to the best approximation properties of the interpolation space. Many gauge field theories can be formulated variationally using a multisymplectic Lagrangian formulation, and we will present a characterization of the exact generating functionals that generate the multisymplectic relation. By discretizing these using group-equivariant spacetime finite element spaces, we obtain methods that exhibit a discrete multimomentum conservation law. We will then briefly describe an approach for constructing group-equivariant interpolation spaces that take values in the space of Lorentzian metrics that can be efficiently computed using a generalized polar decomposition. The goal is to eventually apply this to the construction of variational discretizations of general relativity, which is a second-order gauge field theory whose configuration manifold is the space of Lorentzian metrics.2019-10-01T12:03:02+01:0036003071682true16x9falsenoA Monte Carlo method to sample a Stratificationucs_sms_3028099_3104885http://sms.cam.ac.uk/media/3104885
A Monte Carlo method to sample a StratificationHolmes-Cefron, M
Wednesday 20th November 2019 - 15:40 to 16:10Thu, 21 Nov 2019 15:42:10 +0000Isaac Newton InstituteHolmes-Cefron, M5c49386fc424ca210145ab467f91406604c760a1c7edaabf97db615eecc157357876b4bbc4f8abb7067299243a6a565530808c51f9d176ab00761fcb59758407Holmes-Cefron, M
Wednesday 20th November 2019 - 15:40 to 16:10Holmes-Cefron, M
Wednesday 20th November 2019 - 15:40 to 16:10Cambridge University2688http://sms.cam.ac.uk/media/3104885A Monte Carlo method to sample a StratificationHolmes-Cefron, M
Wednesday 20th November 2019 - 15:40 to 16:10Many problems in materials science and biology involve particles interacting with strong, short-ranged bonds, that can break and form on experimental timescales. Treating such bonds as constraints can significantly speed up sampling their equilibrium distribution, and there are several methods to sample subject to fixed constraints. We introduce a Monte Carlo method to handle the case when constraints can break and form. Abstractly, the method samples a probability distribution on a stratification: a collection of manifolds of different dimensions, where the lower-dimensional manifolds lie on the boundaries of the higher-dimensional manifolds. We show several applications in polymer physics, self-assembly of colloids, and volume calculation.2019-11-21T15:42:11+00:0026883104885true16x9falsenoA new wave-to-wire wave-energy model: from variational principle to compatible space-time discretisationucs_sms_3028099_3032279http://sms.cam.ac.uk/media/3032279
A new wave-to-wire wave-energy model: from variational principle to compatible space-time discretisationBokhove, O
Wednesday 24th July 2019 - 15:00 to 16:00Wed, 24 Jul 2019 16:29:47 +0100Isaac Newton InstituteBokhove, O0c6dc45bb6a746ae30e6d477d8fb892617fa03ccf8c443a2a22b82f4baf864b17495549b2939c41eaf28837592ca32e89ed60979134720ddc9496e538fe5d133Bokhove, O
Wednesday 24th July 2019 - 15:00 to 16:00Bokhove, O
Wednesday 24th July 2019 - 15:00 to 16:00Cambridge University3128http://sms.cam.ac.uk/media/3032279A new wave-to-wire wave-energy model: from variational principle to compatible space-time discretisationBokhove, O
Wednesday 24th July 2019 - 15:00 to 16:00Amplification phenomena in a so-called bore-soliton-splash have led us to develop a novel wave-energy device with wave amplification in a contraction used to enhance wave-activated buoy motion and magnetically-induced energy generation. An experimental proof-of-principle shows that our wave-energy device works. Most importantly, we develop a novel wave-to-wire mathematical model of the combined wave hydrodynamics, wave-activated buoy motion and electric power generation by magnetic induction, from first principles, satisfying one grand variational principle in its conservative limit. Wave and buoy dynamics are coupled via a Lagrange multiplier, which boundary value at the waterline is subtly solved explicitly by imposing incompressibility in a weak sense. Dissipative features, such as electrical wire resistance and nonlinear LED-loads, are added a posteriori. New is also the intricate and compatible (finite-element) space-time discretisation of the linearised dynamics, guaranteeing numerical stability and the correct energy transfer between the three subsystems. Preliminary simulations of our simplified and linearised wave-energy model are encouraging, yet suboptimal, and involve a first study of the resonant behaviour and parameter dependence of the device.2019-07-24T16:29:47+01:0031283032279true16x9falsenoA Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsucs_sms_3028099_3093861http://sms.cam.ac.uk/media/3093861
A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsFarrell, P
Thursday 31st October 2019 - 16:00 to 17:00Mon, 04 Nov 2019 11:29:59 +0000Isaac Newton InstituteFarrell, Pa1e3e266523966c912cec73befaaf5540cd8590c6ceac0beae5dec0390fb8f901039cf25c9ccbc255da39b550c1c3fc02b96caab40164244c8ab806a49734311Farrell, P
Thursday 31st October 2019 - 16:00 to 17:00Farrell, P
Thursday 31st October 2019 - 16:00 to 17:00Cambridge University2960http://sms.cam.ac.uk/media/3093861A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsFarrell, P
Thursday 31st October 2019 - 16:00 to 17:00When approximating PDEs with the finite element method, large sparse linear systems must be solved. The ideal preconditioner yields convergence that is algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed. Achieving this for the stationary Navier-Stokes has proven challenging: LU factorisation is Reynolds-robust but scales poorly with degree of freedom count, while Schur complement approximations such as PCD and LSC degrade as the Reynolds number is increased. Building on ideas of Schöberl, Xu, Zikatanov, Benzi & Olshanskii, in this talk we present the first preconditioner for the Newton linearisation of the stationary Navier–Stokes equations in three dimensions that achieves both optimal complexity and Reynolds-robustness. The scheme combines augmented Lagrangian stabilisation to control the Schur complement, the convection stabilisation proposed by Douglas & Dupont, a divergence-capturing additive Schwarz relaxation method on each level, and a specialised prolongation operator involving non-overlapping local Stokes solves. The properties of the preconditioner are tailored to the divergence-free CG(k)-DG(k-1) discretisation and the appropriate relaxation is derived from considerations of finite element exterior calculus. We present 3D simulations with over one billion degrees of freedom with robust performance from Reynolds numbers 10 to 5000.2019-11-04T11:29:59+00:0029603093861true16x9falsenoA Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsucs_sms_3028099_3095934http://sms.cam.ac.uk/media/3095934
A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsFarrell, P
Thursday 31st October 2019 - 16:00 to 17:00Thu, 07 Nov 2019 09:35:35 +0000Isaac Newton InstituteFarrell, P868be37b494bf964e9f98e921719c82a2d1c68b4a67463ddefbc52150db700a3adcf28ea1fe9a903eb0412d77f2ee3ca2b96caab40164244c8ab806a49734311Farrell, P
Thursday 31st October 2019 - 16:00 to 17:00Farrell, P
Thursday 31st October 2019 - 16:00 to 17:00Cambridge University2960http://sms.cam.ac.uk/media/3095934A Reynolds-robust preconditioner for the 3D stationary Navier-Stokes equationsFarrell, P
Thursday 31st October 2019 - 16:00 to 17:00When approximating PDEs with the finite element method, large sparse linear systems must be solved. The ideal preconditioner yields convergence that is algorithmically optimal and parameter robust, i.e. the number of Krylov iterations required to solve the linear system to a given accuracy does not grow substantially as the mesh or problem parameters are changed. Achieving this for the stationary Navier-Stokes has proven challenging: LU factorisation is Reynolds-robust but scales poorly with degree of freedom count, while Schur complement approximations such as PCD and LSC degrade as the Reynolds number is increased. Building on ideas of Schöberl, Xu, Zikatanov, Benzi & Olshanskii, in this talk we present the first preconditioner for the Newton linearisation of the stationary Navier–Stokes equations in three dimensions that achieves both optimal complexity and Reynolds-robustness. The scheme combines augmented Lagrangian stabilisation to control the Schur complement, the convection stabilisation proposed by Douglas & Dupont, a divergence-capturing additive Schwarz relaxation method on each level, and a specialised prolongation operator involving non-overlapping local Stokes solves. The properties of the preconditioner are tailored to the divergence-free CG(k)-DG(k-1) discretisation and the appropriate relaxation is derived from considerations of finite element exterior calculus. We present 3D simulations with over one billion degrees of freedom with robust performance from Reynolds numbers 10 to 5000.2019-11-07T09:35:35+00:0029603095934true16x9falsenoApplication of the Wiener-Hopf approach to incorrectly posed BVP of plane elasticityucs_sms_3028099_3047363http://sms.cam.ac.uk/media/3047363
Application of the Wiener-Hopf approach to incorrectly posed BVP of plane elasticityGalybin, A
Friday 16th August 2019 - 13:30 to 14:00Mon, 19 Aug 2019 10:34:30 +0100Isaac Newton InstituteGalybin, Ab617ad208a954dee98b663b7e5c5c31e55ee5f9c83b394cee5a7edee6a649320b63ed9e19d3d8ede069c0f0bf891ffb656380dc6cc75a3cba220fa8a4dc2f25aGalybin, A
Friday 16th August 2019 - 13:30 to 14:00Galybin, A
Friday 16th August 2019 - 13:30 to 14:00Cambridge University1825http://sms.cam.ac.uk/media/3047363Application of the Wiener-Hopf approach to incorrectly posed BVP of plane elasticityGalybin, A
Friday 16th August 2019 - 13:30 to 14:002019-08-19T10:34:30+01:0018253047363true16x9falsenoApproximation of eigenvalue problems arising from partial differential equations: examples and counterexamplesucs_sms_3028099_3078387http://sms.cam.ac.uk/media/3078387
Approximation of eigenvalue problems arising from partial differential equations: examples and counterexamplesBoffi, D
Wednesday 9th October 2019 - 15:05 to 15:50Thu, 10 Oct 2019 11:11:30 +0100Isaac Newton InstituteBoffi, D4bfde39ecddfd9ce478d1de68df17f55201c53a24e18bb60a8fdb7a4b7edb4c873973b89a0cf99668f5809fd33c3db4ada4de47717baa908ec127a2b924a0741Boffi, D
Wednesday 9th October 2019 - 15:05 to 15:50Boffi, D
Wednesday 9th October 2019 - 15:05 to 15:50Cambridge University3238http://sms.cam.ac.uk/media/3078387Approximation of eigenvalue problems arising from partial differential equations: examples and counterexamplesBoffi, D
Wednesday 9th October 2019 - 15:05 to 15:50We discuss the finite element approximation of eigenvalue problems arising from elliptic partial differential equations. We present various examples of non-standard schemes, including mixed finite elements, approximation of operators related to the least-squares finite element method, parameter dependent formulations such as those produced by the virtual element method. Each example is studied theoretically; advantages and disadvantages of
each approach are pointed out.2019-10-10T11:11:30+01:0032383078387true16x9falsenoCompatible finite element spaces for metrics with curvatureucs_sms_3028099_3071796http://sms.cam.ac.uk/media/3071796
Compatible finite element spaces for metrics with curvatureChristiansen, S
Tuesday 1st October 2019 - 14:30 to 15:30Tue, 01 Oct 2019 15:38:26 +0100Isaac Newton InstituteChristiansen, S404955b0b3f19b9a61a4d56c081eb52bf0b5c47a6c546908139e6cdbaef919322b9872c1b946c5b8604c7ff92e3341518d6744bbac417ea21c1f0a3523eb5b7aChristiansen, S
Tuesday 1st October 2019 - 14:30 to 15:30Christiansen, S
Tuesday 1st October 2019 - 14:30 to 15:30Cambridge University3550http://sms.cam.ac.uk/media/3071796Compatible finite element spaces for metrics with curvatureChristiansen, S
Tuesday 1st October 2019 - 14:30 to 15:30I will present some new finite element spaces for metrics with integrable curvature. These were obtained in the framework of finite element systems, developed for constructing differential complexes with adequate gluing conditions between the cells of a mesh. The new spaces have a higher regularity than those of Regge calculus, for which the scalar curvature contains measures supported on lower dimensional simplices (Dirac deltas). This is joint work with Kaibo Hu.2019-10-01T15:38:26+01:0035503071796true16x9falsenoComputational geometric optics: Monge-Ampereucs_sms_3028099_3053007http://sms.cam.ac.uk/media/3053007
Computational geometric optics: Monge-AmpereAwanou, G
Wednesday 28th August 2019 - 14:00 to 15:00Thu, 29 Aug 2019 12:34:31 +0100Isaac Newton InstituteAwanou, G844b1b735812162c55ac90c06c38f686600fc38d60ea8df93856662648f2a7b60b74b39597375609537592fe5f5d2f82da7d47b0a8f06200e48174e5ce0c81d8Awanou, G
Wednesday 28th August 2019 - 14:00 to 15:00Awanou, G
Wednesday 28th August 2019 - 14:00 to 15:00Cambridge University2753http://sms.cam.ac.uk/media/3053007Computational geometric optics: Monge-AmpereAwanou, G
Wednesday 28th August 2019 - 14:00 to 15:00I will review recent developments in the numerical resolution of the second boundary value problem for Monge-Ampere type equations and their applications to the design of reflectors and refractors.2019-08-29T12:34:31+01:0027533053007true16x9falsenoComputational methods for simulating inertial particles in discrete incompressible flowsucs_sms_3028099_3035549http://sms.cam.ac.uk/media/3035549
Computational methods for simulating inertial particles in discrete incompressible flowsTapley, B
Tuesday 30th July 2019 - 15:00 to 16:00Wed, 31 Jul 2019 10:40:58 +0100Isaac Newton InstituteTapley, Ba5a9ec7465c2f5b70fb5c792a2a948876ddaeec338f4d6f969b80c3e9d2d5557e3f982dae1da6e76a6caa8651ccff010edf257b7ec8bc07201ee2d74227452b2Tapley, B
Tuesday 30th July 2019 - 15:00 to 16:00Tapley, B
Tuesday 30th July 2019 - 15:00 to 16:00Cambridge University2795http://sms.cam.ac.uk/media/3035549Computational methods for simulating inertial particles in discrete incompressible flowsTapley, B
Tuesday 30th July 2019 - 15:00 to 16:002019-07-31T10:40:58+01:0027953035549true16x9falsenoConformally mapping water waves: top, bottom or sidesucs_sms_3028099_3059113http://sms.cam.ac.uk/media/3059113
Conformally mapping water waves: top, bottom or sidesNachbin, A
Monday 9th September 2019 - 15:00 to 15:30Mon, 09 Sep 2019 16:16:32 +0100Isaac Newton InstituteNachbin, Ab875586561e7aa339b65ac657b1d96fe93404091dab2ab5be0068d9bb8fb1097205c4dac34db6ec8ec250a9a5bef0b44f2bd69d1a0c3839855f0a79d2f505039Nachbin, A
Monday 9th September 2019 - 15:00 to 15:30Nachbin, A
Monday 9th September 2019 - 15:00 to 15:30Cambridge University2065http://sms.cam.ac.uk/media/3059113Conformally mapping water waves: top, bottom or sidesNachbin, A
Monday 9th September 2019 - 15:00 to 15:30I will present a brief overview of recent work showcasing conformal mapping's important role on surface water-wave dynamics. Conformal mapping can be used to flatten the free surface or a highly irregular bottom topography. It has also been used along the sides of forked channel regions, leading to a Boussinesq system with solitary waves on a graph. Mapping a highly variable bottom topography, among other features, allows the construction of a Dirichlet-to-Neumann operator over a polygonal bottom profile. One very recent example applies to a hydrodynamic pilot-wave model, capturing two bouncing droplets confined in cavities, where they can synchronize as nonlinearly coupled oscillators. Finally, on another topic, I will briefly present a very recent result displaying a spectrally accurate finite difference operator. This difference operator is constructed by unconventional means, having in mind complex analytic functions.2019-09-09T16:16:33+01:0020653059113true16x9falsenoConservation laws and Euler operatorsucs_sms_3028099_3060816http://sms.cam.ac.uk/media/3060816
Conservation laws and Euler operatorsHydon, P
Wednesday 11th September 2019 - 14:00 to 15:00Thu, 12 Sep 2019 13:09:50 +0100Isaac Newton InstituteHydon, Pad870f08bd85ac23ad2250167a3f2befd89374d61cf338fda4cf981e247209f8bdbd0f09646eec45e18cd8635b0416b5c343e07076e44e0089f93db30b5c7611Hydon, P
Wednesday 11th September 2019 - 14:00 to 15:00Hydon, P
Wednesday 11th September 2019 - 14:00 to 15:00Cambridge University2911http://sms.cam.ac.uk/media/3060816Conservation laws and Euler operatorsHydon, P
Wednesday 11th September 2019 - 14:00 to 15:00A (local) conservation law of a given system of differential or difference equations is a divergence expression that is zero on all solutions. The Euler operator is a powerful tool in the formal theory of conservation laws that enables key results to be proved simply, including several generalizations of Noether's theorems. This talk begins with a short survey of the main ideas and results. The current method for inverting the divergence operator generates many unnecessary terms by integrating in all directions simultaneously. As a result, symbolic algebra packages create over-complicated representations of conservation laws, making it difficult to obtain efficient conservative finite difference approximations symbolically. A new approach resolves this problem by using partial Euler operators to construct near-optimal representations. The talk explains this approach, which was developed during the GCS programme.2019-09-12T13:09:51+01:0029113060816true16x9falsenoDeep learning as optimal control problems and Riemannian discrete gradient descent.ucs_sms_3028099_3105528http://sms.cam.ac.uk/media/3105528
Deep learning as optimal control problems and Riemannian discrete gradient descent.Celledoni, E
Thursday 21st November 2019 - 15:05 to 15:45Fri, 22 Nov 2019 12:24:08 +0000Isaac Newton InstituteCelledoni, E5224cd68137d3e6d3d48beda943474bae503cdf77d810edbcfd52f34249f0f4735945df8462be417f85df2b1c2883c6c3b719ec0da9990c4dd31b16fa787d5dcCelledoni, E
Thursday 21st November 2019 - 15:05 to 15:45Celledoni, E
Thursday 21st November 2019 - 15:05 to 15:45Cambridge University2893http://sms.cam.ac.uk/media/3105528Deep learning as optimal control problems and Riemannian discrete gradient descent.Celledoni, E
Thursday 21st November 2019 - 15:05 to 15:45We consider recent work where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We review the first order conditions for optimality, and the conditions ensuring optimality after discretisation. This leads to a class of algorithms for solving the discrete optimal control problem which guarantee that the corresponding discrete necessary conditions for optimality are fulfilled. The differential equation setting lends itself to learning additional parameters such as the time discretisation. We explore this extension alongside natural constraints (e.g. time steps lie in a simplex). We compare these deep learning algorithms numerically in terms of induced flow and generalisation ability. References - M Benning, E Celledoni, MJ Ehrhardt, B Owren, CB Schönlieb, Deep learning as optimal control problems: models and numerical methods, JCD.2019-11-22T12:24:08+00:0028933105528true16x9falsenoDeep Neural Networks and Multigrid Methodsucs_sms_3028099_3093854http://sms.cam.ac.uk/media/3093854
Deep Neural Networks and Multigrid MethodsXu, J
Wednesday 30th October 2019 - 14:05 to 15:05Mon, 04 Nov 2019 11:29:33 +0000Isaac Newton InstituteXu, Jd4535e6b3dcd6a01126e23238e2f013fb80239fa0cb0d1a0d9145bf8ed30d401f203509b046bb7fb3d520ff358644fc5012abd412c3425ec18184626a822279aXu, J
Wednesday 30th October 2019 - 14:05 to 15:05Xu, J
Wednesday 30th October 2019 - 14:05 to 15:05Cambridge University3600http://sms.cam.ac.uk/media/3093854Deep Neural Networks and Multigrid MethodsXu, J
Wednesday 30th October 2019 - 14:05 to 15:05In this talk, I will first give an introduction to several models and algorithms from two different fields: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods. I will then explore mathematical relationships between these models and algorithms and demonstrate how such relationships can be used to understand, study and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. In particular, I will demonstrate how a new convolutional neural network known as MgNet, can be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then explore the theoretical and practical potentials of MgNet.2019-11-04T11:29:33+00:0036003093854true16x9falsenoDeep Neural Networks and Multigrid Methodsucs_sms_3028099_3095927http://sms.cam.ac.uk/media/3095927
Deep Neural Networks and Multigrid MethodsXu, J
Wednesday 30th October 2019 - 14:05 to 15:05Thu, 07 Nov 2019 09:34:58 +0000Isaac Newton InstituteXu, Jd0f70e847e381130accee410448b711f4310847d59b10ffa1dcd6b3caf60bf8083469b51357a97c1ddd142b529d70701012abd412c3425ec18184626a822279aXu, J
Wednesday 30th October 2019 - 14:05 to 15:05Xu, J
Wednesday 30th October 2019 - 14:05 to 15:05Cambridge University3600http://sms.cam.ac.uk/media/3095927Deep Neural Networks and Multigrid MethodsXu, J
Wednesday 30th October 2019 - 14:05 to 15:05In this talk, I will first give an introduction to several models and algorithms from two different fields: (1) machine learning, including logistic regression, support vector machine and deep neural networks, and (2) numerical PDEs, including finite element and multigrid methods. I will then explore mathematical relationships between these models and algorithms and demonstrate how such relationships can be used to understand, study and improve the model structures, mathematical properties and relevant training algorithms for deep neural networks. In particular, I will demonstrate how a new convolutional neural network known as MgNet, can be derived by making very minor modifications of a classic geometric multigrid method for the Poisson equation and then explore the theoretical and practical potentials of MgNet.2019-11-07T09:34:58+00:0036003095927true16x9falsenoDetection of high codimensional bifurcations in variational PDEsucs_sms_3028099_3028106http://sms.cam.ac.uk/media/3028106
Detection of high codimensional bifurcations in variational PDEsOffen, C
Wednesday 17th July 2019 - 11:00 to 12:00Wed, 17 Jul 2019 14:49:35 +0100Isaac Newton InstituteOffen, C8ecc3ff8a67deee0e7acdeab0896ade757c06b8dc851b4c4876d48cf7897ffe247f4c108f4a24d0ed795413c2dd61bb759d3f24cba988646a8029cae3a31f651Offen, C
Wednesday 17th July 2019 - 11:00 to 12:00Offen, C
Wednesday 17th July 2019 - 11:00 to 12:00Cambridge University2300http://sms.cam.ac.uk/media/3028106Detection of high codimensional bifurcations in variational PDEsOffen, C
Wednesday 17th July 2019 - 11:00 to 12:00We derive bifurcation test equations for A-series singularities of nonlinear functionals and, based on these equations, we propose a numerical method for detecting high codimensional bifurcations in parameter-dependent PDEs such as parameter-dependent semilinear Poisson equations. As an example, we consider a Bratu-type problem and show how high codimensional bifurcations such as the swallowtail bifurcation can be found numerically.
Lisa Maria Kreusser, Robert I McLachlan, Christian Offen2019-07-17T14:49:35+01:0023003028106true16x9falsenoDiscrete Vector Bundles with Connection and the First Chern Classucs_sms_3028099_3072210http://sms.cam.ac.uk/media/3072210
Discrete Vector Bundles with Connection and the First Chern ClassHirani, A
Wednesday 2nd October 2019 - 09:30 to 10:30Wed, 02 Oct 2019 10:46:27 +0100Isaac Newton InstituteHirani, A94b4cc624f640dc6582de5e37bffdd1a35d0f07fc86f19b6fce852382b05831ee0b30a329652c22f0810d0cebb23ca0f3435901bcb1df6b924987a56007124d5Hirani, A
Wednesday 2nd October 2019 - 09:30 to 10:30Hirani, A
Wednesday 2nd October 2019 - 09:30 to 10:30Cambridge University3780http://sms.cam.ac.uk/media/3072210Discrete Vector Bundles with Connection and the First Chern ClassHirani, A
Wednesday 2nd October 2019 - 09:30 to 10:30The use of differential forms in general relativity requires ingredients like the covariant exterior derivative and curvature. One potential approach to numerical relativity would require discretizations of these ingredients. I will describe a discrete combinatorial theory of vector bundles with connections. The main operator we develop is a discrete covariant exterior derivative that generalizes the coboundary operator and yields a discrete curvature and a discrete Bianchi identity. We test this theory by defining a discrete first Chern class, a topological invariant of vector bundles. This discrete theory is built by generalizing discrete exterior calculus (DEC) which is a discretization of exterior calculus on manifolds for real-valued differential forms. In the first part of the talk I will describe DEC and its applications to the Hodge-Laplace problem and Navier-Stokes equations on surfaces, and then I will develop the discrete covariant exterior derivative and its implications. This is joint work with Daniel Berwick-Evans and Mark Schubel.2019-10-02T10:46:27+01:0037803072210true16x9falsenoEnergy estimates: proving stability for evolving surface PDEs and geometric flowsucs_sms_3028099_3118234http://sms.cam.ac.uk/media/3118234
Energy estimates: proving stability for evolving surface PDEs and geometric flowsKovács, B
Wednesday 4th December 2019 - 14:05 to 14:50Fri, 06 Dec 2019 11:18:26 +0000Isaac Newton InstituteKovács, Bda7ef39820a604f555164160f9dc588f0310583aa534535c81c7f689d539f3218671d61f364afd124f06c65e378e205547fd21a213760f1d30f6f6ec16750f31Kovács, B
Wednesday 4th December 2019 - 14:05 to 14:50Kovács, B
Wednesday 4th December 2019 - 14:05 to 14:50Cambridge University2727http://sms.cam.ac.uk/media/3118234Energy estimates: proving stability for evolving surface PDEs and geometric flowsKovács, B
Wednesday 4th December 2019 - 14:05 to 14:50In this talk we will give some details on the main steps and ideas behind energy estimates used to prove stability of backward difference semi- and full discretisations of parabolic evolving surface problems, or geometric flows (e.g. mean curvature flow). We will give details on how the G-stability result of Dahlquist and the multiplier techniques of Nevanlinna and Odeh will be used.2019-12-06T11:18:26+00:0027273118234true16x9falsenoExterior Shape Calculusucs_sms_3028099_3032070http://sms.cam.ac.uk/media/3032070
Exterior Shape CalculusHiptmair, R
Monday 22nd July 2019 - 14:00 to 15:00Wed, 24 Jul 2019 09:07:17 +0100Isaac Newton InstituteHiptmair, R7822ccfea8098c6bca94a2e70e7048194ce30aacd24985fd54a48700b3bbb551dc788b51e18c7da61edcfa271c0d0abd27c7623d9c3c21e1e72e4f9a2e1dc08aHiptmair, R
Monday 22nd July 2019 - 14:00 to 15:00Hiptmair, R
Monday 22nd July 2019 - 14:00 to 15:00Cambridge University4020http://sms.cam.ac.uk/media/3032070Exterior Shape CalculusHiptmair, R
Monday 22nd July 2019 - 14:00 to 15:002019-07-24T09:07:17+01:0040203032070true16x9falsenoFast approximation on the real lineucs_sms_3028099_3041986http://sms.cam.ac.uk/media/3041986
Fast approximation on the real lineIserles, A
Wednesday 7th August 2019 - 14:00 to 15:00Fri, 09 Aug 2019 15:56:14 +0100Isaac Newton InstituteIserles, A839359290bde620844d11cc8919f30adf6c8fc8c27665a8fe286dfbfc8cf9390c926379bdb56779e2b4d3d7e97e4d1649f973cc7a8f089f43ec593131ebd605fIserles, A
Wednesday 7th August 2019 - 14:00 to 15:00Iserles, A
Wednesday 7th August 2019 - 14:00 to 15:00Cambridge University3287http://sms.cam.ac.uk/media/3041986Fast approximation on the real lineIserles, A
Wednesday 7th August 2019 - 14:00 to 15:00While approximation theory in an interval is thoroughly understood, the real line represents something of a mystery. In this talk we review the state of the art in this area, commencing from the familiar Hermite functions and moving to recent results characterising all orthonormal sets on L2(−∞,∞) that have a skew-symmetric (or skew-Hermitian) tridiagonal differentiation matrix and such that their first n expansion coefficients can be calculated in O(nlogn) operations. In particular, we describe the generalised Malmquist–Takenaka system. The talk concludes with a (too!) long list of open problems and challenges.2019-08-09T15:56:14+01:0032873041986true16x9falsenoFEEC 4 GR?ucs_sms_3028099_3073395http://sms.cam.ac.uk/media/3073395
FEEC 4 GR?Arnold, D
Thursday 3rd October 2019 - 16:00 to 17:00Thu, 03 Oct 2019 17:18:28 +0100Isaac Newton InstituteArnold, Db8f0bdbdaace475e2c98a2c39ea52f2e49b0aa4a4cf016bd2da627252ad6c6680035eab77a5312d7eef153bcfb8adc9522f0b84b25e709b687869912b32f1634Arnold, D
Thursday 3rd October 2019 - 16:00 to 17:00Arnold, D
Thursday 3rd October 2019 - 16:00 to 17:00Cambridge University4440http://sms.cam.ac.uk/media/3073395FEEC 4 GR?Arnold, D
Thursday 3rd October 2019 - 16:00 to 17:00The finite element exterior calculus (FEEC) has proven to be a powerful tool for the design and understanding of numerical methods for solving PDEs from many branches of physics: solid mechanics, fluid flow, electromagnetics, etc. Based on preserving crucial geometric and topological structures underlying the equations, it is a prime example of a structure-preserving numerical method. It has organized many known finite element methods resulting in the periodic table of finite elements. For elasticity, which is not covered by the table, it led to new methods with long sought-after properties. Might the FEEC approach lead to better numerical solutions of the Einstein equations as well? This talk will explore this question through two examples: the Einstein--Bianchi formulation of the Einstein equations based on Bel decomposition of the Weyl tensor, and the Regge elements, a family of finite elements inspired by Regge calculus. Our goal in the talk is to raise questions and inspire future work; we do not purport to provide anything near definitive answers.2019-10-03T17:18:28+01:0044403073395true16x9falsenoFinite element exterior calculus as a tool for compatible discretizations ucs_sms_3028099_3073298http://sms.cam.ac.uk/media/3073298
Finite element exterior calculus as a tool for compatible discretizations Winther, R
Thursday 3rd October 2019 - 14:30 to 15:30Thu, 03 Oct 2019 16:08:10 +0100Isaac Newton InstituteWinther, Rfc795403f1e4b094b349094efecd91ac9181d4b8ef3470675bcaba730da25c2363788f7a45b1838cc9420d2b4cb914a8ac8c974680164bb3c7a2a241f8ba4129Winther, R
Thursday 3rd October 2019 - 14:30 to 15:30Winther, R
Thursday 3rd October 2019 - 14:30 to 15:30Cambridge University3420http://sms.cam.ac.uk/media/3073298Finite element exterior calculus as a tool for compatible discretizations Winther, R
Thursday 3rd October 2019 - 14:30 to 15:30The purpose of this talk is to review the basic results of finite element exterior calculus (FEEC) and to illustrate how the set up gives rise to
to compatible discretizations of various problems. In particular, we will recall how FEEC, combined with the Bernstein-Gelfand-Gelfand framework,
gave new insight into the construction of stable schemes for elasticity methods based on the Hellinger-Reissner variational principle.2019-10-03T16:08:10+01:0034203073298true16x9falsenoFinite element methods for Hamiltonian PDEsucs_sms_3028099_3045975http://sms.cam.ac.uk/media/3045975
Finite element methods for Hamiltonian PDEsStern, A
Wednesday 14th August 2019 - 15:00 to 16:00Fri, 16 Aug 2019 15:17:29 +0100Isaac Newton InstituteStern, A5db4018ab4c8b4b25c74fc8340c0cf11a6157911898954141aeb2d24f881d71ee923e26be0abbf3c59f1b1cf6e922fb519c7fcad9a6da0a3f70ff544fa5b4414Stern, A
Wednesday 14th August 2019 - 15:00 to 16:00Stern, A
Wednesday 14th August 2019 - 15:00 to 16:00Cambridge University3340http://sms.cam.ac.uk/media/3045975Finite element methods for Hamiltonian PDEsStern, A
Wednesday 14th August 2019 - 15:00 to 16:00Hamiltonian ODEs satisfy a symplectic conservation law, and there are many advantages to using numerical integrators that preserves this structure. This talk will discuss how the canonical Hamiltonian structure, and its preservation by a numerical method, can be generalized to PDEs. I will also provide a basic introduction to the finite element method and, time permitting, discuss how some classic symplectic integrators can be understood from this point of view.2019-08-16T15:17:29+01:0033403045975true16x9falsenoHigh-order splitting for the Vlasov-Poisson equationucs_sms_3028099_3093759http://sms.cam.ac.uk/media/3093759
High-order splitting for the Vlasov-Poisson equationFaou, E
Monday 28th October 2019 - 10:00 to 10:45Mon, 04 Nov 2019 10:14:41 +0000Isaac Newton InstituteFaou, E2a293b439124dffc8c4182f72f0155a7a328be5e093f28bdd18f05d9ed5dc70b64e45e1fc57872e7bd3e96ea519baaec9eba1aa9aab449f2118a8a3b3c1fcb12Faou, E
Monday 28th October 2019 - 10:00 to 10:45Faou, E
Monday 28th October 2019 - 10:00 to 10:45Cambridge University2828http://sms.cam.ac.uk/media/3093759High-order splitting for the Vlasov-Poisson equationFaou, E
Monday 28th October 2019 - 10:00 to 10:45We consider the Vlasov{Poisson equation in a Hamiltonian framework and
derive time splitting methods based on the decomposition of the Hamiltonian functional
between the kinetic and electric energy. We also apply a similar strategy to the Vlasov{
Maxwell system. These are joint works with N. Crouseilles, F. Casas, M. Mehrenberger
and L. Einkemmer.2019-11-04T10:14:41+00:0028283093759true16x9falsenoHybrid Monte Carlo methods for sampling probability measures on submanifoldsucs_sms_3028099_3104609http://sms.cam.ac.uk/media/3104609
Hybrid Monte Carlo methods for sampling probability measures on submanifoldsLelievre, T
Wednesday 20th November 2019 - 13:50 to 14:30Thu, 21 Nov 2019 10:36:03 +0000Isaac Newton InstituteLelievre, Tfaf565e15194972193fc21d50198f8d0b0e0b849cc2b4299dae08a1e2dbd332712df95efda6214fc2485244ea85eb4133d353ad940fd277ee87445064f43646dLelievre, T
Wednesday 20th November 2019 - 13:50 to 14:30Lelievre, T
Wednesday 20th November 2019 - 13:50 to 14:30Cambridge University2721http://sms.cam.ac.uk/media/3104609Hybrid Monte Carlo methods for sampling probability measures on submanifoldsLelievre, T
Wednesday 20th November 2019 - 13:50 to 14:30Various applications require the sampling of probability measures restricted to submanifolds defined as the level set of some functions, in particular in computational statistical physics. We will present recent results on so-called Hybrid Monte Carlo methods, which consists in adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In order to avoid biases in the invariant probability measures sampled by discretizations of these stochastically perturbed Hamiltonian dynamics, a Metropolis rejection procedure can be considered. The so-obtained scheme belongs to the class of generalized Hybrid Monte Carlo (GHMC) algorithms, and we will discuss how to ensure that the sampling method is unbiased in practice.
References:
- T. Lelièvre, M. Rousset and G. Stoltz, Langevin dynamics with constraints and computation of free energy differences, Mathematics of Computation, 81(280), 2012.
- T. Lelièvre, M. Rousset and G. Stoltz, Hybrid Monte Carlo methods for sampling probability measures on submanifolds, to appear in Numerische Mathematik, 2019.
- E. Zappa, M. Holmes-Cerfon, and J. Goodman. Monte Carlo on manifolds: sampling densities and integrating functions. Communications in Pure and Applied Mathematics, 71(12), 2018.2019-11-21T10:36:03+00:0027213104609true16x9falsenoHyponormal quantization of planar domainsucs_sms_3028099_3060915http://sms.cam.ac.uk/media/3060915
Hyponormal quantization of planar domainsPutinar, M
Thursday 12th September 2019 - 14:00 to 15:00Thu, 12 Sep 2019 15:07:21 +0100Isaac Newton InstitutePutinar, M3724468cafd6291feac0ebd6e82201ee440a0e51de9c55d40902a62cf32c3ab48b7ee513f226479f62fad4874bb7b720f5ed33fd0aab5a1fea04f1589668f34e6e57bdc903a38f457b3e108d91c2cb12Putinar, M
Thursday 12th September 2019 - 14:00 to 15:00Putinar, M
Thursday 12th September 2019 - 14:00 to 15:00Cambridge University3780http://sms.cam.ac.uk/media/3060915Hyponormal quantization of planar domainsPutinar, M
Thursday 12th September 2019 - 14:00 to 15:00By replacing the identity operator in Heisenberg commutation relation [T*,T]=I by a rank-one projection one unveils an accessible spectral analysis classification with singular integrals of Cauchy type as generic examples. An inverse spectral problem for this class of (hyponormal) operators can be invoked for encoding and decoding (partial) data of 2D pictures carrying a grey shade function. An exponential transform, the two dimensional analog of a similar operation on Cauchy integrals introduced by A, Markov in his pioneering work on 1D moment problems, provides an effective dictionary between "pictures" in the frequency domain and "matrices" in the state space interpretation. A natural Riemann-Hilbert problem lies at the origin of this kernel with potential theoretic flavor. Quadrature domains for analytic functions are singled out by a rationality property of the exponential transform, and hence an exact reconstruction algorithm for this class of black and white shapes emerges. A two variable diagonal Pade approximation scheme and some related complex orthogonal polynomials enter into the picture, with their elusive zero asymptotics. Most of the results streaming from two decades of joint work with Bjorn Gustafsson.2019-09-12T15:07:21+01:0037803060915true16x9falsenoInside the Final Black Hole from Black Hole Collisionsucs_sms_3028099_3073887http://sms.cam.ac.uk/media/3073887
Inside the Final Black Hole from Black Hole CollisionsLaguna, P
Friday 4th October 2019 - 11:00 to 12:00Fri, 04 Oct 2019 12:13:44 +0100Isaac Newton InstituteLaguna, Pfc0ee138c7b71d3b2f1e50a24830d9d4ade187c34f8ce81ae94f9d83eb02379c3dcf4b53848ec41e578c83a75717f59c3ec9d4da217d3f0845d90704965c2a2bLaguna, P
Friday 4th October 2019 - 11:00 to 12:00Laguna, P
Friday 4th October 2019 - 11:00 to 12:00Cambridge University3960http://sms.cam.ac.uk/media/3073887Inside the Final Black Hole from Black Hole CollisionsLaguna, P
Friday 4th October 2019 - 11:00 to 12:00Modeling black hole singularities as punctures in space-time is common in binary black hole simulations. As the punctures approach each other, a common apparent horizon forms, signaling the coalescence of the black holes and the formation of the final black hole. I will present results from a study that investigates the fate of the punctures and in particular the dynamics of the trapped surfaces on each puncture.
Co-authors: Christopher Evans, Deborah Ferguson, Bhavesh Khamesra and Deirdre Shoemaker2019-10-04T12:13:44+01:0039603073887true16x9falsenoKirk Lecture: A recent technology for Scientific Computing: the Virtual Element Methoducs_sms_3028099_3084641http://sms.cam.ac.uk/media/3084641
Kirk Lecture: A recent technology for Scientific Computing: the Virtual Element MethodMarini, D
Monday 21st October 2019 - 16:00 to 17:00Mon, 21 Oct 2019 16:58:56 +0100Isaac Newton InstituteMarini, D4816b7c2016b1532d0b99b544d91c902cbd3a9a341a519ddd55c3805a4257c34607153aa922abcba615a05168d4563667d214f3d22510436982cc0ad98d56e80Marini, D
Monday 21st October 2019 - 16:00 to 17:00Marini, D
Monday 21st October 2019 - 16:00 to 17:00Cambridge University3260http://sms.cam.ac.uk/media/3084641Kirk Lecture: A recent technology for Scientific Computing: the Virtual Element MethodMarini, D
Monday 21st October 2019 - 16:00 to 17:00The Virtual Element Method (VEM) is a recent technology for the numerical solution of boundary value problems for Partial Differential Equations. It could be seen as a generalization of the Finite Element Method (FEM). With FEM the computational domain is typically split in triangles/quads (tetrahedra/hexahedra). VEM responds to the recent interest in using decompositions into polygons/polyhedra of very general shape, whenever more convenient for the approximation of problems of practical interest. Indeed,the possibility of using general polytopal meshes opens up a new range of opportunities in terms of accuracy, efficiency and flexibility. This is for instance reflected by the fact that various (commercial and free) codes recently included and keep developing polytopal meshes, showing in selected applications an improved computational efficiency with respect to tetrahedral or hexahedral grids. In this talk, after a general description of the use and potential of Scientific Computing, basic ideas of conforming VEM will be described on a simple model problem. Numerical results on more general problems in two and three dimension will be shown. Hints on Serendipity versions will be given at the end. These procedures allow to decrease significantly the number of degrees of freedom, that is, to reduce the dimension of the final linear system.2019-10-21T16:58:56+01:0032603084641true16x9falsenoLow-regularity time integratorsucs_sms_3028099_3102884http://sms.cam.ac.uk/media/3102884
Low-regularity time integratorsOstermann, A
Wednesday 13th November 2019 - 16:00 to 17:00Mon, 18 Nov 2019 11:20:26 +0000Isaac Newton InstituteOstermann, A1fb3389300929a8e53cc83cbe6551a2cc3f9aafe5cd6a645db1c400985154fcdab666e7ef8dfa8f35d9b55da1e144c277a5406ae1b3382b23b0070d5af2ecc3bOstermann, A
Wednesday 13th November 2019 - 16:00 to 17:00Ostermann, A
Wednesday 13th November 2019 - 16:00 to 17:00Cambridge University3720http://sms.cam.ac.uk/media/3102884Low-regularity time integratorsOstermann, A
Wednesday 13th November 2019 - 16:00 to 17:00Nonlinear Schrödinger equations are usually solved by pseudo-spectral methods, where the time integration is performed by splitting schemes or exponential integrators. Notwithstanding the benefits of this approach, its successful application requires additional regularity of the solution. For instance, second-order Strang splitting requires four additional derivatives for the solution of the cubic nonlinear Schrödinger equation. Similar statements can be made about other dispersive equations like the Korteweg-de Vries or the Boussinesq equation. In this talk, we introduce low-regularity Fourier integrators as an alternative. They are obtained from Duhamel's formula in the following way: first, a Lawson-type transformation eliminates the leading linear term and second, the dominant nonlinear terms are integrated exactly in Fourier space. For cubic nonlinear Schrödinger equations, first-order convergence of such methods only requires the boundedness of one additional derivative of the solution, and second-order convergence the boundedness of two derivatives. Similar improvements can also be obtained for other dispersive problems. This is joint work with Frédéric Rousset (Université Paris-Sud), Katharina Schratz (Hariot-Watt, UK), and Chunmei Su (Technical University of Munich).2019-11-18T11:20:26+00:0037203102884true16x9falsenoMagnus, splitting and composition techniques for solving non-linear Schrödinger equationsucs_sms_3028099_3100184http://sms.cam.ac.uk/media/3100184
Magnus, splitting and composition techniques for solving non-linear Schrödinger equationsBlanes, S
Monday 11th November 2019 - 16:00 to 17:00Wed, 13 Nov 2019 08:43:21 +0000Isaac Newton InstituteBlanes, S4e7389abf5cc213a8fa8f38017b30542f7d9747d7eb41acc31fb420180a428435ee8ec5ac926b053dde890c14fd03bd89d16020426f37f2e763274e9f9d97bcbBlanes, S
Monday 11th November 2019 - 16:00 to 17:00Blanes, S
Monday 11th November 2019 - 16:00 to 17:00Cambridge University2888http://sms.cam.ac.uk/media/3100184Magnus, splitting and composition techniques for solving non-linear Schrödinger equationsBlanes, S
Monday 11th November 2019 - 16:00 to 17:00In this talk I will consider several non-autonomous non-linear Schrödinger equations
(the Gross-Pitaevskii equation, the Kohn-Sham equation and an Quantum Optimal Control equation)
and some of the numerical methods that have been used to solve them.
With a proper linearization of these equations we end up with non-autonomous linear systems
where many of the algebraic techniques from Magnus, splitting and composition algorithms can be used.
This will be an introductory talk to stimulate some collaboration between participants of the program
at the INI.2019-11-13T08:43:21+00:0028883100184true16x9falsenoMixed order and multirate variational integrators for the simulation of dynamics on different time scalesucs_sms_3028099_3056801http://sms.cam.ac.uk/media/3056801
Mixed order and multirate variational integrators for the simulation of dynamics on different time scalesLeyendecker, S
Wednesday 4th September 2019 - 15:00 to 16:00Thu, 05 Sep 2019 12:21:58 +0100Isaac Newton InstituteLeyendecker, S49ba145e7f69a56041ab6be070f8ab472452f410bd54e24c5f31ca82b7bba8ebc0c6a24a9288cc74aa873c0a56986492aa748bd3f2cc7e568e907fc4ead786dbLeyendecker, S
Wednesday 4th September 2019 - 15:00 to 16:00Leyendecker, S
Wednesday 4th September 2019 - 15:00 to 16:00Cambridge University3384http://sms.cam.ac.uk/media/3056801Mixed order and multirate variational integrators for the simulation of dynamics on different time scalesLeyendecker, S
Wednesday 4th September 2019 - 15:00 to 16:00Mechanical systems with dynamics on varying time scales, e.g. including highly oscillatory motion, impose challenging questions for numerical integration schemes. High resolution is required to guarantee a stable integration of the fast frequencies. However, for the simulation of the slow dynamics, integration with a lower resolution is accurate enough - and computationally cheaper, especially for costly function evaluations. Two approaches are presented, a mixed order Galerkin variational integrator and a multirate variational integrator, and analysed with respect to the preservation of invariants, computational costs, accuracy and linear stability.2019-09-05T12:21:58+01:0033843056801true16x9falsenoModelling processes in landscapes - Van Oijen, Mucs_sms_3028099_3036130http://sms.cam.ac.uk/media/3036130
Modelling processes in landscapes - Van Oijen, MVan Oijen, M
Wednesday 31st July 2019 - 15:30 to 16:00Wed, 31 Jul 2019 16:51:20 +0100Isaac Newton InstituteVan Oijen, Md21bd392e6465c4601d3058ff0b739d74f4aa6ec49763bbb69ecfcc598f610f2c118c01affbbbbc22198afbceee33ae11aef264ba6b0a0c7a60a5e18e499d13cVan Oijen, M
Wednesday 31st July 2019 - 15:30 to 16:00Van Oijen, M
Wednesday 31st July 2019 - 15:30 to 16:00Cambridge University1812http://sms.cam.ac.uk/media/3036130Modelling processes in landscapes - Van Oijen, MVan Oijen, M
Wednesday 31st July 2019 - 15:30 to 16:002019-07-31T16:51:21+01:0018123036130true16x9falsenoMore on composition methods: error estimation and pseudo-symmetryucs_sms_3028099_3049612http://sms.cam.ac.uk/media/3049612
More on composition methods: error estimation and pseudo-symmetryCasas, F
Wednesday 21st August 2019 - 14:00 to 15:00Thu, 22 Aug 2019 14:03:05 +0100Isaac Newton InstituteCasas, Ffad5a6bf06622b7d8aa1446c3d4910bc26d4ab4e9c391b4ccf1226f4f572a6b139ac43a2676b3b194271a1e5ff7ec6fac6602f8b1da81f2fd4c4127da91f5d3fCasas, F
Wednesday 21st August 2019 - 14:00 to 15:00Casas, F
Wednesday 21st August 2019 - 14:00 to 15:00Cambridge University3011http://sms.cam.ac.uk/media/3049612More on composition methods: error estimation and pseudo-symmetryCasas, F
Wednesday 21st August 2019 - 14:00 to 15:00In this talk I will review composition methods for the time integration of differential equations,
paying special attention to two recent contributions in this area. The first one is the construction
of a new local error estimator so that the additional computational effort required is almost insignificant.
The second one is related to a new family of high-order methods obtained from a basic symmetric
(symplectic) scheme in such a way that they are time-symmetric (symplectic) only up to a certain order.2019-08-22T14:03:06+01:0030113049612true16x9falsenoNewest Results in Newest Vertex Bisectionucs_sms_3028099_3093726http://sms.cam.ac.uk/media/3093726
Newest Results in Newest Vertex BisectionLicht, M
Wednesday 25th September 2019 - 14:05 to 14:50Mon, 04 Nov 2019 09:03:21 +0000Isaac Newton InstituteLicht, M4171eb961a3f3c7f9474078e51f5818b218bc4a7112711d244418b2a34eea68c1cffe59a73860829c4bc51ed84778dbf6abc56e5233fa5c68301cab55e2472fdLicht, M
Wednesday 25th September 2019 - 14:05 to 14:50Licht, M
Wednesday 25th September 2019 - 14:05 to 14:50Cambridge University3229http://sms.cam.ac.uk/media/3093726Newest Results in Newest Vertex BisectionLicht, M
Wednesday 25th September 2019 - 14:05 to 14:50The algorithmic refinement of triangular meshes is an important component in numerical simulation codes. Newest vertex bisection is one of the most popular methods for geometrically stable local refinement. Its complexity analysis, however, is a fairly intricate recent result and many combinatorial aspects of this method are not yet fully understood. In this talk, we access newest vertex bisection from the perspective of theoretical computer science. We outline the amortized complexity analysis over generalized triangulations. An immediate application is the convergence and complexity analysis of adaptive finite element methods over embedded surfaces and singular surfaces. Moreover, we "combinatorialize" the complexity estimate and remove any geometry-dependent constants, which is only natural for this purely combinatorial algorithm and improves upon prior results. This is joint work with Michael Holst and Zhao Lyu.2019-11-04T09:03:21+00:0032293093726true16x9falsenoNumerical approximations of a tractable mathematical model for tissue growthucs_sms_3028099_3118241http://sms.cam.ac.uk/media/3118241
Numerical approximations of a tractable mathematical model for tissue growthStyles, V
Thursday 5th December 2019 - 13:30 to 14:15Fri, 06 Dec 2019 11:20:18 +0000Isaac Newton InstituteStyles, V8d745258be995f1c33e98e33a89dcdf3b4655806403a9cb0f650d019f1d0fe6d4d96152d99bac9ec0f39b65154f651bc3ab595d4df5e5f643e3aa48e81d37278Styles, V
Thursday 5th December 2019 - 13:30 to 14:15Styles, V
Thursday 5th December 2019 - 13:30 to 14:15Cambridge University2549http://sms.cam.ac.uk/media/3118241Numerical approximations of a tractable mathematical model for tissue growthStyles, V
Thursday 5th December 2019 - 13:30 to 14:15We consider a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour. The mathematical model takes the form of a closed interface evolving via forced mean curvature flow where the forcing depends on the solution of a PDE that holds in the domain enclosed by the interface. We derive sharp interface and diffuse interface finite element approximations of this model and present some numerical results2019-12-06T11:20:18+00:0025493118241true16x9falsenoNumerical Computation of Hausdorff Dimensionucs_sms_3028099_3078374http://sms.cam.ac.uk/media/3078374
Numerical Computation of Hausdorff DimensionFalk, R
Wednesday 9th October 2019 - 14:05 to 14:50Thu, 10 Oct 2019 11:10:29 +0100Isaac Newton InstituteFalk, R27de4252501e331635ee5a6f5199dad4d4ce3a48a494391893f3963bdc1a78fe153aded63846c0ec9bbc06221ab93ad09170cf0187f0e7524a7568a4f77f027dFalk, R
Wednesday 9th October 2019 - 14:05 to 14:50Falk, R
Wednesday 9th October 2019 - 14:05 to 14:50Cambridge University2543http://sms.cam.ac.uk/media/3078374Numerical Computation of Hausdorff DimensionFalk, R
Wednesday 9th October 2019 - 14:05 to 14:50We show how finite element approximation theory can be combined with theoretical results about the properties of the eigenvectors of a class of linear Perron-Frobenius operators to obtain accurate approximations of the Hausdorff dimension of some invariant sets arising from iterated function systems.
The theory produces rigorous upper and lower bounds on the Hausdorff dimension. Applications to the computation of the Hausdorff dimension of some Cantor sets arising from real and complex continued fraction expansions are described.2019-10-10T11:10:29+01:0025433078374true16x9falsenoNumerical General Relativityucs_sms_3028099_3045967http://sms.cam.ac.uk/media/3045967
Numerical General RelativityGarfinkle, D
Wednesday 14th August 2019 - 14:00 to 15:00Fri, 16 Aug 2019 15:15:43 +0100Isaac Newton InstituteGarfinkle, D76fe40b633e06fd8f57409d04ebc35bb6eea979c786e254c85d17f5181e1525de346084f8cc0f3b5ffc110fb51a9242498f51c0ac9424fcd6a8f242fa7cfddf3Garfinkle, D
Wednesday 14th August 2019 - 14:00 to 15:00Garfinkle, D
Wednesday 14th August 2019 - 14:00 to 15:00Cambridge University3311http://sms.cam.ac.uk/media/3045967Numerical General RelativityGarfinkle, D
Wednesday 14th August 2019 - 14:00 to 15:00This talk will cover the basic properties of the equations of General Relativity, and issues involved in performing numerical simulations of those equations. Particular emphasis will be placed on three issues: (1) hyperbolicity of the equations. (2) preserving constraints. (3) dealing with black holes and spacetime singularities.2019-08-16T15:15:43+01:0033113045967true16x9falsenoNumerical Integrators for the Hamiltonian Monte Carlo Methoducs_sms_3028099_3057336http://sms.cam.ac.uk/media/3057336
Numerical Integrators for the Hamiltonian Monte Carlo MethodSanz-Serna, C
Thursday 5th September 2019 - 14:15 to 15:15Fri, 06 Sep 2019 12:50:26 +0100Isaac Newton InstituteSanz-Serna, C4e04ca087e3a5de4e402ea42e19e1ea821c41986dcc16bf08ff0bc7e3e1cd5a880ed426d126928974e3e218e1a2d3fcd69804033601eb3c4672842a0cc5de3a4Sanz-Serna, C
Thursday 5th September 2019 - 14:15 to 15:15Sanz-Serna, C
Thursday 5th September 2019 - 14:15 to 15:15Cambridge University3578http://sms.cam.ac.uk/media/3057336Numerical Integrators for the Hamiltonian Monte Carlo MethodSanz-Serna, C
Thursday 5th September 2019 - 14:15 to 15:152019-09-06T12:50:26+01:0035783057336true16x9falsenoNumerical preservation of local conservation lawsucs_sms_3028099_3060823http://sms.cam.ac.uk/media/3060823
Numerical preservation of local conservation lawsFrasca-Caccia, G
Wednesday 11th September 2019 - 15:00 to 16:00Thu, 12 Sep 2019 13:10:26 +0100Isaac Newton InstituteFrasca-Caccia, G949844513583d6c53fceea503cb88baac7a9e38e4d712685390a5656289224d155ea4dcc947f2a095bb6e94bd68a4465e8d707d54ac76a67489cb798bcccbc69Frasca-Caccia, G
Wednesday 11th September 2019 - 15:00 to 16:00Frasca-Caccia, G
Wednesday 11th September 2019 - 15:00 to 16:00Cambridge University2903http://sms.cam.ac.uk/media/3060823Numerical preservation of local conservation lawsFrasca-Caccia, G
Wednesday 11th September 2019 - 15:00 to 16:00In the numerical treatment of partial differential equations (PDEs), the benefits of preserving global integral invariants are well-known. Preserving the underlying local conservation law gives, in general, a stricter constraint than conserving the global invariant obtained by integrating it in space. Conservation laws, in fact, hold throughout the domain and are satisfied by all solutions, independently of initial and boundary conditions. A new approach that uses symbolic algebra to develop bespoke finite difference schemes that preserve multiple local conservation laws has been recently applied to PDEs with polynomial nonlinearity. The talk illustrates this new strategy using some well-known equations as benchmark examples and shows comparisons between the obtained schemes and other integrators known in literature.2019-09-12T13:10:26+01:0029033060823true16x9falsenoNumerical Relativity in the Era of Gravitational Wave Observationsucs_sms_3028099_3070921http://sms.cam.ac.uk/media/3070921
Numerical Relativity in the Era of Gravitational Wave ObservationsShoemaker, D
Monday 30th September 2019 - 09:30 to 10:30Mon, 30 Sep 2019 10:40:24 +0100Isaac Newton InstituteShoemaker, D6c5fb9fe2d35cd8440479992fa35dcd352a3eeac696d56a8891a4b00da3ee7ef7bc13a31553b446bcda52327bb5d970c1b757948bca412e50fb809f70c13a8b6Shoemaker, D
Monday 30th September 2019 - 09:30 to 10:30Shoemaker, D
Monday 30th September 2019 - 09:30 to 10:30Cambridge University3780http://sms.cam.ac.uk/media/3070921Numerical Relativity in the Era of Gravitational Wave ObservationsShoemaker, D
Monday 30th September 2019 - 09:30 to 10:30The birth and future of gravitational wave astronomy offers new opportunities and challenges for numerical methods in general relativity. Numerical relativity in particular provides critical support to detect and interpret gravitational wave measurements. In this talk, I’ll discuss the role numerical relativity is playing in the observed black hole binaries by LIGO and Virgo and its future potential for unveiling strong-field gravity in future detections with an emphasis on the computational challenges. I'll frame a discussion about what demands will be placed on this field to maximize the science output of the new era.2019-09-30T10:40:24+01:0037803070921true16x9falsenoOn numerical conservation of the Poincaré-Cartan integral invariant in relativistic fluid dynamicsucs_sms_3028099_3073946http://sms.cam.ac.uk/media/3073946
On numerical conservation of the Poincaré-Cartan integral invariant in relativistic fluid dynamicsMarkakis, C
Friday 4th October 2019 - 13:30 to 14:30Fri, 04 Oct 2019 14:21:17 +0100Isaac Newton InstituteMarkakis, C55eaa57f8569676f90d2200a604d8738b15eecdb731943d94e42adcfe29ae4e3b13e13e31ca9adcff90ad2dff8dea6d991d2622f289e8801d18d16e62aaa0c85Markakis, C
Friday 4th October 2019 - 13:30 to 14:30Markakis, C
Friday 4th October 2019 - 13:30 to 14:30Cambridge University2383http://sms.cam.ac.uk/media/3073946On numerical conservation of the Poincaré-Cartan integral invariant in relativistic fluid dynamicsMarkakis, C
Friday 4th October 2019 - 13:30 to 14:30The motion of strongly gravitating fluid bodies is described by the Euler-Einstein system of partial differential equations. We report progress on formulating well-posed, acoustical and canonical hydrodynamic schemes, suitable for binary inspiral simulations and gravitational-wave source modelling. The schemes use a variational principle by Carter-Lichnerowicz stating that barotropic fluid motions are conformally geodesic, a corollary to Kelvin's theorem stating that initially irrotational flows remain irrotational, and Christodoulou's acoustic metric approach adopted to numerical relativity, in order to evolve the canonical momentum of a fluid element via Hamilton or Hamilton-Jacobi equations. These mathematical theorems leave their imprints on inspiral waveforms from binary neutron stars observed by the LIGO-Virgo detectors. We describe a constraint damping scheme for preserving circulation in numerical general relativity, in accordance with Helmholtz's third theorem.2019-10-04T14:21:17+01:0023833073946true16x9falsenoOn structure-preserving particle-in-cell methods for the Vlasov-Maxwell equationsucs_sms_3028099_3093766http://sms.cam.ac.uk/media/3093766
On structure-preserving particle-in-cell methods for the Vlasov-Maxwell equationsKormann, K
Monday 28th October 2019 - 10:45 to 11:30Mon, 04 Nov 2019 10:16:28 +0000Isaac Newton InstituteKormann, Kb2874c0ffde3e15ffae80e390fc88242d7931abf9c753d1cb11b22313702369127092215bf83a2e6ce0e23ff83af70bab8f19234246421b6bcf0fc2902666bbeKormann, K
Monday 28th October 2019 - 10:45 to 11:30Kormann, K
Monday 28th October 2019 - 10:45 to 11:30Cambridge University2991http://sms.cam.ac.uk/media/3093766On structure-preserving particle-in-cell methods for the Vlasov-Maxwell equationsKormann, K
Monday 28th October 2019 - 10:45 to 11:30Numerical schemes that preserve the structure of the kinetic equations can
provide new insight into the long time behavior of fusion plasmas. An electromagnetic
particle-in-cell solver for the Vlasov{Maxwell equations that preserves at the discrete
level the non-canonical Hamiltonian structure of the Vlasov{Maxwell equations has
been presented in [1]. In this talk, the framework of this geometric particle-in-cell
method will be presented and extension to curvilinear coordinates will be discussed.
Moreover, various options for the temporal discretizations will be proposed and compared.
[1] M. Kraus, K. Kormann, P. J. Morrison, and E. Sonnendrucker. GEMPIC: geometric electromag-
netic particle-in-cell methods. Journal of Plasma Physics, 83(4), 2017.2019-11-04T10:16:28+00:0029913093766true16x9falsenoOn the construction of some symplectic P-stable additive Runge—Kutta methodsucs_sms_3028099_3124310http://sms.cam.ac.uk/media/3124310
On the construction of some symplectic P-stable additive Runge—Kutta methodsZanna, A
Wednesday 11th December 2019 - 14:05 to 14:50Mon, 16 Dec 2019 16:03:51 +0000Isaac Newton InstituteZanna, Aa32362359b2425775f2d9339d7ede16ee972f21a93276dd7a8c00994ee38efc02dc7cb2c34edd224bcf7e731e3154df94df70fb10b2302cbb0f2f87c9e31abfaZanna, A
Wednesday 11th December 2019 - 14:05 to 14:50Zanna, A
Wednesday 11th December 2019 - 14:05 to 14:50Cambridge University2938http://sms.cam.ac.uk/media/3124310On the construction of some symplectic P-stable additive Runge—Kutta methodsZanna, A
Wednesday 11th December 2019 - 14:05 to 14:50Symplectic partitioned Runge–Kutta methods can be obtained from a variational formulation treating all the terms in the Lagrangian with the same quadrature formula. We construct a family of symplectic methods allowing the use of different quadrature formula for different parts of the Lagrangian. In particular, we study a family of methods using Lobatto quadrature (with corresponding Lobatto IIIA-IIIB symplectic method) and Gauss–Legendre quadrature combined in an appropriate way. The resulting methods are similar to additive Runge-Kutta methods. The IMEX method, using the Verlet and IMR combination is a particular case of this family. The methods have the same favourable implicitness as the underlying Lobatto IIIA-IIIB pair. Differently from the Lobatto IIIA-IIIB, which are known not to be P-stable, we show that the new methods satisfy the requirements for P-stability.2019-12-16T16:03:51+00:0029383124310true4x3falsenoOn the nature of mathematical joyucs_sms_3028099_3111717http://sms.cam.ac.uk/media/3111717
On the nature of mathematical joyMansfield, E
Thursday 28th November 2019 - 16:00 to 17:00Thu, 28 Nov 2019 16:49:07 +0000Isaac Newton InstituteMansfield, Ef0e17561188158a2d103fcafd65a628ddb8be4630b32ef38d6ab04844f09e5b40f278abcb94b1bc648dad19aab174edd1c7d4cebd9d59bd750455de577bfec8cMansfield, E
Thursday 28th November 2019 - 16:00 to 17:00Mansfield, E
Thursday 28th November 2019 - 16:00 to 17:00Cambridge University2541http://sms.cam.ac.uk/media/3111717On the nature of mathematical joyMansfield, E
Thursday 28th November 2019 - 16:00 to 17:00Elizabeth Mansfield will discuss seven levels of mathematical joy based on her mathematical travels. This is a talk for a general audience.2019-11-28T16:49:07+00:0025413111717true16x9falsenoOn the Solvability Complexity Index (SCI) hierarchy - Establishing the foundations of computational mathematics ucs_sms_3028099_3110069http://sms.cam.ac.uk/media/3110069
On the Solvability Complexity Index (SCI) hierarchy - Establishing the foundations of computational mathematics Hansen, A
Tuesday 26th November 2019 - 15:05 to 16:05Tue, 26 Nov 2019 16:04:30 +0000Isaac Newton InstituteHansen, A79c3a52ae7f5a9b6fff8249600002f1718040bc03546e0b4a76bb9ef3b2b1698c8a00555d652db3aa84dbb347de8a9475191028bcd92504b6e0e9d59b5bf27f8Hansen, A
Tuesday 26th November 2019 - 15:05 to 16:05Hansen, A
Tuesday 26th November 2019 - 15:05 to 16:05Cambridge University3334http://sms.cam.ac.uk/media/3110069On the Solvability Complexity Index (SCI) hierarchy - Establishing the foundations of computational mathematics Hansen, A
Tuesday 26th November 2019 - 15:05 to 16:05There are four areas in computational mathematics that have been intensely investigated over more than half a century: Spectral problems, PDEs, optimisation and inverse problems. However, despite the matureness of these fields, the foundations are far from known. Indeed, despite almost 90 years of quantum mechanics, it is still unknown whether it is possible to compute the spectrum of a self-adjoint Schrodinger operator with a bounded smooth potential. Similarly, it is not known which time dependent Schrodinger equations can be computed (despite well posedness of the equation). Linear programs (LP) can be solved with rational inputs in polynomial time, but can LPs be solved with irrational inputs? Problems in signal and image processing tend to use irrational numbers, so what happens if one plugs in the discrete cosine transform in one's favourite LP solver? Moreover, can one always compute the solutions to well-conditioned infinite-dimensional inverse problems, and if not, which inverse problems can then be solved? In this talk we will discuss solutions to many of the questions above, and some of the results may seem paradoxical. Indeed, despite being an open problem for more than half a century, computing spectra of Schrodinger operators with a bounded potential is not harder than computing spectra of infinite diagonal matrices, the simplest of all infinite-dimensional spectral problems. Moreover, computing spectra of compact operators, for which the method has been known for decades, is strictly harder than computing spectra of such Schrodinger operators. Regarding linear programs (and basis pursuit, semidefinite programs and LASSO) we have the following. For any integer K > 2 and any norm, there exists a family of well conditioned inputs containing irrational numbers so that no algorithm can compute K correct digits of a minimiser, however, there exists an algorithm that can compute K-1 correct digits. But any algorithm producing K-1 correct digits will need arbitrarily long time. Finally, computing K-2 correct digits can be done in polynomial time in the number of variables. As we will see, all of these problems can be solved via the the Solvability Complexity Index (SCI) hierarchy, which is a theoretical program for establishing the boundaries of what computers can achieve in the sciences.2019-11-26T16:04:30+00:0033343110069true16x9falsenoPhase field modelling of free boundary problemsucs_sms_3028099_3118248http://sms.cam.ac.uk/media/3118248
Phase field modelling of free boundary problemsStinner, B
Thursday 5th December 2019 - 14:15 to 15:00Fri, 06 Dec 2019 11:23:59 +0000Isaac Newton InstituteStinner, Ba3d708203863b2d5de61423e7bfe701eb901051c7f1b2b7a98ad7efa9c11b0afd894a19e4ba176a8e33fa2e799df82c2eb7bac25e572404ef98bccc254a890d0Stinner, B
Thursday 5th December 2019 - 14:15 to 15:00Stinner, B
Thursday 5th December 2019 - 14:15 to 15:00Cambridge University2801http://sms.cam.ac.uk/media/3118248Phase field modelling of free boundary problemsStinner, B
Thursday 5th December 2019 - 14:15 to 15:00Diffuse interface models based on the phase field methodology have been developed and investigated in various applications such as solidification processes, tumour growth, or multi-phase flow. The interfaces are represented by thin layers, across which quantities rapidly but smoothly change their values. These interfacial layers are described in terms of order parameters, the equations for which can be solved using relatively straightforward methods, such as finite elements with adaptive mesh refinement, as no tracking of any interface is required. The interface motion is usually coupled to other fields and equations adjacent or on the interface, for instance, diffusion equations in alloys or the momentum equation in fluid flow. We discuss how such systems can be incorporated into phase field models in a generic way. Furthermore, we present a computational framework where specific models can be implemented and later on conveniently amended, if desired, in a high-level language, and which then bind to efficient software backends. A couple of code listings and numerical simulations serve to illustrate the approach2019-12-06T11:23:59+00:0028013118248true16x9falsenoRandom Batch Methods for Interacting Particle Systems and Consensus-based Global Non-convex Optimization in High-dimensional Machine Learning (copy)ucs_sms_3028099_3100177http://sms.cam.ac.uk/media/3100177
Random Batch Methods for Interacting Particle Systems and Consensus-based Global Non-convex Optimization in High-dimensional Machine Learning (copy)Jin, S
Monday 11th November 2019 - 14:00 to 15:00Wed, 13 Nov 2019 08:43:26 +0000Isaac Newton InstituteJin, S1c7f7316b2002464d5bfc5e1e08ce1edc46f6cc34a42b56fda2c0aea4f853f9e58fe89cf6cb9f3ec255ac97232dd54fe63be86cce1e9f62cc753d32bcaa1614aJin, S
Monday 11th November 2019 - 14:00 to 15:00Jin, S
Monday 11th November 2019 - 14:00 to 15:00Cambridge University3263http://sms.cam.ac.uk/media/3100177Random Batch Methods for Interacting Particle Systems and Consensus-based Global Non-convex Optimization in High-dimensional Machine Learning (copy)Jin, S
Monday 11th November 2019 - 14:00 to 15:00We develop random batch methods for interacting particle systems with large number of particles. These methods
use small but random batches for particle interactions,
thus the computational cost is reduced from O(N^2) per time step to O(N), for a
system with N particles with binary interactions.
For one of the methods, we give a particle number independent error estimate under some special interactions.
Then, we apply these methods
to some representative problems in mathematics, physics, social and data sciences, including the Dyson Brownian
motion from random matrix theory, Thomson's problem,
distribution of wealth, opinion dynamics and clustering. Numerical results show that
the methods can capture both the transient solutions and the global equilibrium in
these problems.
We also apply this method and improve the consensus-based global optimization algorithm for high
dimensional machine learning problems. This method does not require taking gradient in finding global
minima for non-convex functions in high dimensions.2019-11-13T08:43:26+00:0032633100177true16x9falsenoRothschild Lecture: Hamiltonian Monte Carlo and geometric integrationucs_sms_3028099_3118443http://sms.cam.ac.uk/media/3118443
Rothschild Lecture: Hamiltonian Monte Carlo and geometric integrationSanz-Serna, C
Friday 6th December 2019 - 16:00 to 17:00Fri, 06 Dec 2019 17:03:15 +0000Isaac Newton InstituteSanz-Serna, Ca8baed80fdc92b3e913d7cff16a31a164d6ed431e2d9d84da1a22b6de3b04ad46f4f884c3afcf7cdd54ae461c4d87a597f628db186aa32fa6cfc0c153e3c5af1Sanz-Serna, C
Friday 6th December 2019 - 16:00 to 17:00Sanz-Serna, C
Friday 6th December 2019 - 16:00 to 17:00Cambridge University3324http://sms.cam.ac.uk/media/3118443Rothschild Lecture: Hamiltonian Monte Carlo and geometric integrationSanz-Serna, C
Friday 6th December 2019 - 16:00 to 17:00Many application fields require samples from an arbitrary probability distribution. Hamiltonian Monte Carlo is a sampling algorithm that originated in the physics literature and has later gained much popularity among statisticians. This is a talk addressed to a general audience, where I will describe the algorithm and some of its applications. The exposition requires basic ideas from different fields, from statistical physics to geometric integration of differential equations and from Bayesian statistics to Hamiltonian dynamics and I will provide the necessary background, albeit superficially.2019-12-06T17:03:15+00:0033243118443true16x9falsenoSerendipity Virtual Elementsucs_sms_3028099_3085016http://sms.cam.ac.uk/media/3085016
Serendipity Virtual ElementsBrezzi, F
Tuesday 22nd October 2019 - 09:05 to 09:50Tue, 22 Oct 2019 09:59:01 +0100Isaac Newton InstituteBrezzi, Fe009285b33e49b39ff9641cf96ff6a0efad6b381a19a1e6c71230376fb743d33bd3826ddd860632a9d764ab7ec0aaab4981c8fa9e6162d19eb1bbf9b80be8b42Brezzi, F
Tuesday 22nd October 2019 - 09:05 to 09:50Brezzi, F
Tuesday 22nd October 2019 - 09:05 to 09:50Cambridge University2982http://sms.cam.ac.uk/media/3085016Serendipity Virtual ElementsBrezzi, F
Tuesday 22nd October 2019 - 09:05 to 09:50After a brief reminder of classical ("plain vanilla") Virtual Elements we will see the general philosophy of "enhanced Virtual Elements" and the various types of Serendipity spaces as particular cases. The construction will always be conceptually simple (and extremely powerful, in particular for polygons with many edges), but a code exploiting the full advantage of having many edges might become difficult in the presence of non convex polygons, and in particular for complicated shapes. We shall also discuss different choices ensuring various advantages for different amounts of work.2019-10-22T09:59:01+01:0029823085016true16x9falsenoSolving PDEs Numerically on Manifolds with Arbitrary Spatial Topologiesucs_sms_3028099_3071587http://sms.cam.ac.uk/media/3071587
Solving PDEs Numerically on Manifolds with Arbitrary Spatial TopologiesLindblom, L
Tuesday 1st October 2019 - 09:30 to 10:30Tue, 01 Oct 2019 10:36:05 +0100Isaac Newton InstituteLindblom, Lda71cfbd5596e4770be9ef7059e1e95e539fb4d4bcc8f4315b302ee75430f7f18f2dac5caf179bc33497b604a433da66c3513b92c047087abf6dd830817fbd1eLindblom, L
Tuesday 1st October 2019 - 09:30 to 10:30Lindblom, L
Tuesday 1st October 2019 - 09:30 to 10:30Cambridge University3600http://sms.cam.ac.uk/media/3071587Solving PDEs Numerically on Manifolds with Arbitrary Spatial TopologiesLindblom, L
Tuesday 1st October 2019 - 09:30 to 10:302019-10-01T10:36:05+01:0036003071587true16x9falsenoSome results in the long time analysis of Hamiltonian PDEs and their numerical approximationsucs_sms_3028099_3100255http://sms.cam.ac.uk/media/3100255
Some results in the long time analysis of Hamiltonian PDEs and their numerical approximationsFaou, E
Tuesday 12th November 2019 - 16:00 to 17:00Wed, 13 Nov 2019 09:37:45 +0000Isaac Newton InstituteFaou, E665afd63e3a94ca1c1de0be5a48b1e26871aebeb2cf6b53efc3032c8f777c2d6dee8f20cadb64c3036729c81f35689257f78749a3d2d4abc2c3c7c2755d4f666Faou, E
Tuesday 12th November 2019 - 16:00 to 17:00Faou, E
Tuesday 12th November 2019 - 16:00 to 17:00Cambridge University3451http://sms.cam.ac.uk/media/3100255Some results in the long time analysis of Hamiltonian PDEs and their numerical approximationsFaou, E
Tuesday 12th November 2019 - 16:00 to 17:00I will review some results concerning the long time behavior of Hamiltonian PDEs, and address
similar questions for their numerical approximation. I will show numerical resonances can appear
both in space and time. I will also discuss the long time stability of solitary waves evolving
on a discret set of lattice points.2019-11-13T09:37:45+00:0034513100255true16x9falsenoSome thoughts about constrained sampling algorithmsucs_sms_3028099_3105604http://sms.cam.ac.uk/media/3105604
Some thoughts about constrained sampling algorithmsLeimkuhler, B
Thursday 21st November 2019 - 13:50 to 14:30Fri, 22 Nov 2019 12:41:53 +0000Isaac Newton InstituteLeimkuhler, B47fccca4fbd6948c5b4d60b7b537a06cd0a3d153ced7331cb03ac0dce8363fb0270a263f691dcf4ec0921e39a322ebc166fae10168106187522c8da9a9dd0eb3Leimkuhler, B
Thursday 21st November 2019 - 13:50 to 14:30Leimkuhler, B
Thursday 21st November 2019 - 13:50 to 14:30Cambridge University2838http://sms.cam.ac.uk/media/3105604Some thoughts about constrained sampling algorithmsLeimkuhler, B
Thursday 21st November 2019 - 13:50 to 14:30I will survey our work on algorithms for sampling diffusions on manifolds, including isokinetic methods and constrained Langevin dynamics methods. These have mostly been introduced and tested in the setting of molecular dynamics. It is interesting to consider possible uses of these ideas in other types of sampling computations, like neural network parameterization and training of generative models.2019-11-22T12:41:53+00:0028383105604true16x9falsenoSpatial/temporal scaling - Comber. Aucs_sms_3028099_3036116http://sms.cam.ac.uk/media/3036116
Spatial/temporal scaling - Comber. AComber. A
Wednesday 31st July 2019 - 12:30 to 13:00Wed, 31 Jul 2019 16:51:18 +0100Isaac Newton InstituteComber. Ab721d2d5fd0fe6bb37223a595d4600cb392a878a7c52c310ed2b8dedeecf34fbf276f6cdf4437725d6b22d2ac416826608b109bc3fb48385db59c74a44164ea4Comber. A
Wednesday 31st July 2019 - 12:30 to 13:00Comber. A
Wednesday 31st July 2019 - 12:30 to 13:00Cambridge University1928http://sms.cam.ac.uk/media/3036116Spatial/temporal scaling - Comber. AComber. A
Wednesday 31st July 2019 - 12:30 to 13:002019-07-31T16:51:18+01:0019283036116true16x9falsenoSpectral deferred correction in particle-in-cell methodsucs_sms_3028099_3093773http://sms.cam.ac.uk/media/3093773
Spectral deferred correction in particle-in-cell methodsNiesen, J
Monday 28th October 2019 - 15:15 to 16:00Mon, 04 Nov 2019 10:16:03 +0000Isaac Newton InstituteNiesen, J6ff3f0e456650e59e19900ad75f08273e46fc998772f10ac7af5c9d79d72bd8c533ef969039eaeb00af64b6e4e6e1b6dd93dfbe0ca08b55f6c3d671f73675306Niesen, J
Monday 28th October 2019 - 15:15 to 16:00Niesen, J
Monday 28th October 2019 - 15:15 to 16:00Cambridge University2326http://sms.cam.ac.uk/media/3093773Spectral deferred correction in particle-in-cell methodsNiesen, J
Monday 28th October 2019 - 15:15 to 16:00Particle-in-cell methods solve the Maxwell equations for the electromagnetic
eld in combination with the equation of motion for the charged particles in a
plasma. The motion of charegd particles is usually computed using the Boris algorithm,
a variant of Stormer{Verlet for Lorentz force omputations, which has impressive
performance and order two (like Stormer{Verlet). Spectral deferred correction is an
iterative time stepping method based on collocation, which in each time step performs
multiple sweeps of a low-order method (here, the Boris method) in order to obtain a
high-order approximation. This talk describes the ongoing eorts of Kristoer Smedt,
Daniel Ruprecht, Steve Tobias and the speaker to embed a spectral deferred correction
time stepper based on the Boris method in a particle-in-cell method.2019-11-04T10:16:03+00:0023263093773true16x9falsenoStep size control for Newton type MCMC samplers Jonathan Goodmanucs_sms_3028099_3105414http://sms.cam.ac.uk/media/3105414
Step size control for Newton type MCMC samplers Jonathan GoodmanGoodman, J
Wednesday 20th November 2019 - 15:05 to 15:35Fri, 22 Nov 2019 08:43:44 +0000Isaac Newton InstituteGoodman, Jedd49735d590519f60dbb4a0f60e1f4e5905c60256154cfdf0e6c29b48bf3d84a6d611d2d923a49e2aa959a881338736756773249c93335ac36431ca379ff7d7Goodman, J
Wednesday 20th November 2019 - 15:05 to 15:35Goodman, J
Wednesday 20th November 2019 - 15:05 to 15:35Cambridge University1347http://sms.cam.ac.uk/media/3105414Step size control for Newton type MCMC samplers Jonathan GoodmanGoodman, J
Wednesday 20th November 2019 - 15:05 to 15:35ABSTRACT: MCMC sampling can use ideas from the optimization community. Optimization via Newton’s method can fail without line search, even for smooth strictly convex problems. Affine invariant Newton based MCMC sampling uses a Gaussian proposal based on a quadratic model of the potential using the local gradient and Hessian. This can fail (conjecture: give a transient Markov chain) even for smooth strictly convex potentials. We describe a criterion that allows a sequence of proposal distributions from X_n with decreasing “step sizes” until (with probability 1) a proposal is accepted. “Very detailed balance” allows the whole process to preserve the target distribution. The method works in experiments but the theory is missing.2019-11-22T08:43:44+00:0013473105414true16x9falsenoSymmetry Preserving Interpolationucs_sms_3028099_3110053http://sms.cam.ac.uk/media/3110053
Symmetry Preserving InterpolationHubert, E
Tuesday 26th November 2019 - 14:05 to 14:50Tue, 26 Nov 2019 15:29:30 +0000Isaac Newton InstituteHubert, Efea8517f0b5d787adfcbc275ffa732b48203c45a3b3082dc59ec71b664e7fac2754701b8dcf97c89f4928a30b72378a34885fc008e50be1bc35ba218b095a172Hubert, E
Tuesday 26th November 2019 - 14:05 to 14:50Hubert, E
Tuesday 26th November 2019 - 14:05 to 14:50Cambridge University3150http://sms.cam.ac.uk/media/3110053Symmetry Preserving InterpolationHubert, E
Tuesday 26th November 2019 - 14:05 to 14:50In this talk I choose to present the PhD work of Erick Rodriguez Bazan. We address multivariate interpolation in the presence of symmetry as given by a finite group. Interpolation is a prime tool in algebraic computation while symmetry is a qualitative feature
that can be more relevant to a mathematical model than the numerical accuracy of the parameters. Beside its preservation, symmetry shall also be exploited to alleviate the computational cost.
We revisit minimal degree and least interpolation spaces [de Boor & Ron 1990] with symmetry adapted bases (rather than the usual monomial bases). In these bases, the multivariate Vandermonde matrix (a.k.a colocation matrix) is block diagonal as soon as the set of nodes is invariant. These blocks capture the inherent redundancy in the computations. Furthermore any equivariance an interpolation problem might have will be automatically preserved : the output interpolant will have the same equivariance property.
The special case of multivariate Hermite interpolation leads us to question the representation of polynomial ideals. Gröbner bases, the preferred tool for algebraic computations, breaks any kind of symmetry. The prior notion of H-Bases, introduced by Macaulay, appears as more suitable.
Reference:
https://dl.acm.org/citation.cfm?doid=3326229.3326247
https://hal.inria.fr/hal-01994016 Joint work with Erick Rodriguez Bazan2019-11-26T15:29:30+00:0031503110053true16x9falsenotbaucs_sms_3028099_3074002http://sms.cam.ac.uk/media/3074002
tbaLehner, L
Friday 4th October 2019 - 14:30 to 15:30Fri, 04 Oct 2019 15:56:29 +0100Isaac Newton InstituteLehner, L453c372e5c73774e4c1301fb3aebcec86df84cf35824fbe6565892dd706416f22269dbab36764a7a4417b72eddaf9e97356c0b4b8e7c91d0b884774a92977e86Lehner, L
Friday 4th October 2019 - 14:30 to 15:30Lehner, L
Friday 4th October 2019 - 14:30 to 15:30Cambridge University3720http://sms.cam.ac.uk/media/3074002tbaLehner, L
Friday 4th October 2019 - 14:30 to 15:302019-10-04T15:56:29+01:0037203074002true16x9falsenoThe Connections Between Discrete Geometric Mechanics, Information Geometry and Machine Learningucs_sms_3028099_3035542http://sms.cam.ac.uk/media/3035542
The Connections Between Discrete Geometric Mechanics, Information Geometry and Machine LearningLeok, M
Tuesday 30th July 2019 - 14:00 to 15:00Wed, 31 Jul 2019 12:11:43 +0100Isaac Newton InstituteLeok, M92a7e3fde732dcb159e0fa04eece472167ce64178ae87c7b46e7413ef3931c62be1ce33fc5d56f168dce1c8dc7194ba93d6b939aabc076dac4676c7b7b6826eeLeok, M
Tuesday 30th July 2019 - 14:00 to 15:00Leok, M
Tuesday 30th July 2019 - 14:00 to 15:00Cambridge University3335http://sms.cam.ac.uk/media/3035542The Connections Between Discrete Geometric Mechanics, Information Geometry and Machine LearningLeok, M
Tuesday 30th July 2019 - 14:00 to 15:002019-07-31T12:11:44+01:0033353035542true16x9falsenoUPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTION-DIFFUSION PROBLEMSucs_sms_3028099_3085214http://sms.cam.ac.uk/media/3085214
UPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTION-DIFFUSION PROBLEMSXu, J
Tuesday 22nd October 2019 - 13:55 to 14:40Tue, 22 Oct 2019 14:56:16 +0100Isaac Newton InstituteXu, J57b0cfee898b940f3b2197f9a6382f8d1d0e793d5d9f7aff9f3d8f6d610597bea94af433d1713537fae8a0ba72c6298225a55c4d5e0f633c7a903283d8ab1431Xu, J
Tuesday 22nd October 2019 - 13:55 to 14:40Xu, J
Tuesday 22nd October 2019 - 13:55 to 14:40Cambridge University3009http://sms.cam.ac.uk/media/3085214UPWIND FINITE ELEMENT METHODS FOR H(grad), H(curl) AND H(div) CONVECTION-DIFFUSION PROBLEMSXu, J
Tuesday 22nd October 2019 - 13:55 to 14:40This talk is devoted to the construction and analysis of the finite element approximations for the H(grad), H(curl) and H(div) convection-diffusion problems. An essential feature of these constructions is to properly average the PDE coefficients on sub-simplexes from the underlying simplicial finite element meshes. The schemes are of the class of exponential fitting methods that result in special upwind schemes when the diffusion coefficient approaches to zero. Their well-posedness are established for sufficiently small mesh size assuming that the convection-diffusion problems are uniquely solvable. Convergence of first order is derived under minimal smoothness of the solution. Some numerical examples are given to demonstrate the robustness and effectiveness for general convection-diffusion problems. This is a joint work with Shounan Wu.2019-10-22T14:56:17+01:0030093085214true16x9falsenoVariational formulations for dissipative systemsucs_sms_3028099_3056794http://sms.cam.ac.uk/media/3056794
Variational formulations for dissipative systemsOber-Blöbaum, S
Wednesday 4th September 2019 - 14:00 to 15:00Thu, 05 Sep 2019 12:21:22 +0100Isaac Newton InstituteOber-Blöbaum, Sbcfd5fd5508a536b92b08de4327b3ee171c81f7c8493ea660814f55bc0d1779c8ed0ce8d970a8fdcf46ed7fea6b29630230b8c232812c6888146e962a79dcfc1Ober-Blöbaum, S
Wednesday 4th September 2019 - 14:00 to 15:00Ober-Blöbaum, S
Wednesday 4th September 2019 - 14:00 to 15:00Cambridge University3056http://sms.cam.ac.uk/media/3056794Variational formulations for dissipative systemsOber-Blöbaum, S
Wednesday 4th September 2019 - 14:00 to 15:00Variational principles are powerful tools for the modelling and simulation of conservative mechanical and electrical systems. As it is well-known, the fulfilment of a variational principle leads to the Euler-Lagrange equations of motion describing the dynamics of such systems. Furthermore, a variational discretisation directly yields unified numerical schemes with powerful structure-preserving properties. Since many years there have been several attempts to provide a variational description also for dissipative mechanical systems, a task that is addressed in the talk in order to construct both Lagrangian and Hamiltonian pictures of their dynamics. One way doing this is to use fractional terms in the Lagrangian or Hamiltonian function which allows for a purely variational derivation of dissipative systems. Another approach followed in this talk is to embed the non-conservative systems in larger conservative systems. These concepts are used to develop variational integrators for which superior qualitative numerical properties such as the correct energy dissipation rate are demonstrated.2019-09-05T12:21:22+01:0030563056794true16x9falsenoWhat it takes to catch a wave packetucs_sms_3028099_3102867http://sms.cam.ac.uk/media/3102867
What it takes to catch a wave packetLasser, C
Wednesday 13th November 2019 - 14:00 to 15:00Mon, 18 Nov 2019 11:18:21 +0000Isaac Newton InstituteLasser, C9100c7d65aed9639893fcc848ef818a59e9d0adbd91853e55359cbcac516cd95b0e6113ffb124020f747a37a37ff648db6a76fe0f08e1b6ed4f56b4f659d8bedLasser, C
Wednesday 13th November 2019 - 14:00 to 15:00Lasser, C
Wednesday 13th November 2019 - 14:00 to 15:00Cambridge University3900http://sms.cam.ac.uk/media/3102867What it takes to catch a wave packetLasser, C
Wednesday 13th November 2019 - 14:00 to 15:00Wave packets describe the quantum vibrations of a molecule. They are highly oscillatory,
highly localized and move in high dimensional configuration spaces. The talk addresses
three meshless numerical methods for catching them: single Gaussian beams,
superpositions of them, and the so-called linearized initial value representation.2019-11-18T11:18:22+00:0039003102867true16x9falseno3028099